Use a sum or difference identity to find the EXACT value: sin ⁡ ( 15 ° ) \sin\left(15\degree\right) sin ( 1 5 ° )

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: sin ⁡ ( 75 ° ) \sin\left(75\degree\right) sin ( 7 5 ° )

2 + 6 4 \frac{\sqrt{2}+\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: cos ⁡ ( 75 ° ) \cos\left(75\degree\right) cos ( 7 5 ° )

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: cos ⁡ ( 105 ° ) \cos\left(105\degree\right) cos ( 1 0 5 ° )

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: cos ⁡ ( π 12 ) \cos\left(\frac{\pi}{12}\right) cos ( 1 2 π )

2 + 6 4 \frac{\sqrt{2}+\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: sin ⁡ ( 7 π 12 ) \sin\left(\frac{7\pi}{12}\right) sin ( 1 2 7 π )

6 + 2 4 \frac{\sqrt{6}+\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Use a sum or difference identity to find the EXACT value: cos ⁡ ( 7 π 12 ) \cos\left(\frac{7\pi}{12}\right) cos ( 1 2 7 π )

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Write the expression as the sine or cosine of a single angle: sin ⁡ 42 ° cos ⁡ 17 ° − cos ⁡ 42 ° sin ⁡ 17 ° \sin42\degree\cos17\degree-\cos42\degree\sin17\degree sin 4 2 ° cos 1 7 ° − cos 4 2 ° sin 1 7 °

sin ⁡ ( 25 ° ) \sin\left(25\degree\right) sin ( 2 5 ° )

sin ⁡ ( 59 ° ) \sin\left(59\degree\right) sin ( 5 9 ° )

cos ⁡ ( 59 ° ) \cos\left(59\degree\right) cos ( 5 9 ° )

cos ⁡ ( 25 ° ) \cos\left(25\degree\right) cos ( 2 5 ° )

Write the expression as the sine or cosine of a single angle: cos ⁡ 94 ° cos ⁡ 18 ° + sin ⁡ 94 ° sin ⁡ 18 ° \cos94\degree\cos18\degree+\sin94\degree\sin18\degree cos 9 4 ° cos 1 8 ° + sin 9 4 ° sin 1 8 °

cos ⁡ ( 76 ° ) \cos\left(76\degree\right) cos ( 7 6 ° )

sin ⁡ ( 76 ° ) \sin\left(76\degree\right) sin ( 7 6 ° )

cos ⁡ ( 112 ° ) \cos\left(112\degree\right) cos ( 1 1 2 ° )

sin ⁡ ( 112 ° ) \sin\left(112\degree\right) sin ( 1 1 2 ° )

Write the expression as the sine or cosine of a single angle: sin ⁡ ( π 5 ) cos ⁡ ( π 2 ) + sin ⁡ ( π 2 ) cos ⁡ ( π 5 ) \sin\left(\frac{\pi}{5}\right)\cos\left(\frac{\pi}{2}\right)+\sin\left(\frac{\pi}{2}\right)\cos\left(\frac{\pi}{5}\right) sin ( 5 π ) cos ( 2 π ) + sin ( 2 π ) cos ( 5 π )

sin ⁡ ( 7 π 10 ) \sin\left(\frac{7\pi}{10}\right) sin ( 1 0 7 π )

cos ⁡ ( 3 π 10 ) \cos\left(\frac{3\pi}{10}\right) cos ( 1 0 3 π )

sin ⁡ ( 3 π 10 ) \sin\left(\frac{3\pi}{10}\right) sin ( 1 0 3 π )

cos ⁡ ( 7 π 10 ) \cos\left(\frac{7\pi}{10}\right) cos ( 1 0 7 π )

Write the expression as the sine or cosine of a single angle: sin ⁡ ( π 3 ) cos ⁡ ( π 7 ) − sin ⁡ ( π 7 ) cos ⁡ ( π 3 ) \sin\left(\frac{\pi}{3}\right)\cos\left(\frac{\pi}{7}\right)-\sin\left(\frac{\pi}{7}\right)\cos\left(\frac{\pi}{3}\right) sin ( 3 π ) cos ( 7 π ) − sin ( 7 π ) cos ( 3 π )

sin ⁡ ( 4 π 21 ) \sin\left(\frac{4\pi}{21}\right) sin ( 2 1 4 π )

cos ⁡ ( 4 π 21 ) \cos\left(\frac{4\pi}{21}\right) cos ( 2 1 4 π )

cos ⁡ ( 10 π 21 ) \cos\left(\frac{10\pi}{21}\right) cos ( 2 1 1 0 π )

sin ⁡ ( 10 π 21 ) \sin\left(\frac{10\pi}{21}\right) sin ( 2 1 1 0 π )

Write the expression as the sine or cosine of a single angle: cos ⁡ ( π 7 ) cos ⁡ x + sin ⁡ ( π 7 ) sin ⁡ x \cos\left(\frac{\pi}{7}\right)\cos x+\sin\left(\frac{\pi}{7}\right)\sin x cos ( 7 π ) cos x + sin ( 7 π ) sin x

cos ⁡ ( π 7 − x ) \cos\left(\frac{\pi}{7}-x\right) cos ( 7 π − x )

sin ⁡ ( π 7 − x ) \sin\left(\frac{\pi}{7}-x\right) sin ( 7 π − x )

cos ⁡ ( π 7 + x ) \cos\left(\frac{\pi}{7}+x\right) cos ( 7 π + x )

sin ⁡ ( π 7 + x ) \sin\left(\frac{\pi}{7}+x\right) sin ( 7 π + x )

Write the expression as the sine or cosine of a single angle: cos ⁡ x cos ⁡ 15 ° − sin ⁡ x sin ⁡ 15 ° \cos x\cos15\degree-\sin x\sin15\degree cos x cos 1 5 ° − sin x sin 1 5 °

cos ⁡ ( x + 15 ° ) \cos\left(x+15\degree\right) cos ( x + 1 5 ° )

cos ⁡ ( x − 15 ° ) \cos\left(x-15\degree\right) cos ( x − 1 5 ° )

sin ⁡ ( x − 15 ° ) \sin\left(x-15\degree\right) sin ( x − 1 5 ° )

sin ⁡ ( x + 15 ° ) \sin\left(x+15\degree\right) sin ( x + 1 5 ° )

Write the expression as the sine or cosine of a single angle: sin ⁡ ( 3 x ) cos ⁡ x − cos ⁡ ( 3 x ) sin ⁡ x \sin\left(3x\right)\cos x-\cos\left(3x\right)\sin x sin ( 3 x ) cos x − cos ( 3 x ) sin x

sin ⁡ ( 2 x ) \sin\left(2x\right) sin ( 2 x )

cos ⁡ ( 2 x ) \cos\left(2x\right) cos ( 2 x )

cos ⁡ ( 4 x ) \cos\left(4x\right) cos ( 4 x )

sin ⁡ ( 4 x ) \sin\left(4x\right) sin ( 4 x )

Write the expression as the sine or cosine of a single angle: cos ⁡ ( 7 y ) cos ⁡ ( 3 y ) − sin ⁡ ( 7 y ) sin ⁡ ( 3 y ) \cos\left(7y\right)\cos\left(3y\right)-\sin\left(7y\right)\sin\left(3y\right) cos ( 7 y ) cos ( 3 y ) − sin ( 7 y ) sin ( 3 y )

cos ⁡ ( 10 y ) \cos\left(10y\right) cos ( 1 0 y )

cos ⁡ ( 4 y ) \cos\left(4y\right) cos ( 4 y )

sin ⁡ ( 4 y ) \sin\left(4y\right) sin ( 4 y )

sin ⁡ ( 10 y ) \sin\left(10y\right) sin ( 1 0 y )

Angle Sum/Difference Identities

Quiz

•

Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.TF.C.9, HSG.SRT.C.8, HSF.TF.A.3

Standards-aligned

Adam Hosler

Used 117+ times

FREE Resource

20 questions

Show all answers

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$15\degree$

$75\degree-60\degree$

$115\degree-100\degree$

$60\degree-45\degree$

$85\degree-70\degree$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$75\degree$

$80\degree-5\degree$

$40\degree+35\degree$

$100\degree-25\degree$

$30\degree+45\degree$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$165\degree$

$185\degree-20\degree$

$45\degree+120\degree$

$35\degree+130\degree$

$180\degree-15\degree$

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.C.8

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$105\degree$

$120\degree-15\degree$

$180\degree-75\degree$

$55\degree+50\degree$

$60\degree+45\degree$

Tags

CCSS.HSF.TF.A.3

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$255\degree$

$200\degree+55\degree$

$220\degree+35\degree$

$300\degree-45\degree$

$360\degree-105\degree$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Use a sum or difference identity to find the EXACT value:

$\sin\left(15\degree\right)$

0.2588

0.6503

$\frac{\sqrt{6}-\sqrt{2}}{4}$

$\frac{\sqrt{2}-\sqrt{6}}{4}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Use a sum or difference identity to find the EXACT value:
$\sin\left(75\degree\right)$

-0.3879

0.9659

$\frac{\sqrt{2}-\sqrt{6}}{4}$

$\frac{\sqrt{2}+\sqrt{6}}{4}$

Tags

CCSS.HSF.TF.C.9

Create a free account and access millions of resources

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

15 questions

Bienvenida

Quiz

•

11th Grade

18 questions

Order of operations

Quiz

•

10th Grade

20 questions

Hoán vị - Chỉnh hợp - Tổ hợp

Quiz

•

11th Grade

20 questions

Latihan Soal "Proyeksi Vektor"

Quiz

•

11th Grade

15 questions

10 ஆம் வகுப்பு கணிதம் பயிற்சி 2.10 ஆக்கம் கோ.இளவரசு

Quiz

•

10th Grade

19 questions

Funciones lineales

Quiz

•

9th - 11th Grade

20 questions

operaciones números complejos

Quiz

•

11th Grade

19 questions

summative test 2

Quiz

•

11th Grade

Popular Resources on Wayground

5 questions

This is not a...winter edition (Drawing game)

Quiz

•

1st - 5th Grade

15 questions

4:3 Model Multiplication of Decimals by Whole Numbers

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

The Best Christmas Pageant Ever Chapters 1 & 2

Quiz

•

4th Grade

12 questions

Unit 4 Review Day

Quiz

•

3rd Grade

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

20 questions

Christmas Trivia

Quiz

•

6th - 8th Grade

18 questions

Kids Christmas Trivia

Quiz

•

KG - 5th Grade

Discover more resources for Mathematics

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

10 questions

Guess the Christmas Movie by the Scene Challenge

Interactive video

•

6th - 10th Grade

11 questions

Solve Systems of Equations and Inequalities

Quiz

•

9th - 12th Grade

10 questions

Test Your Christmas Trivia Skills

Interactive video

•

6th - 10th Grade

17 questions

Identify Linear and Nonlinear Functions

Quiz

•

8th - 12th Grade

10 questions

Fraction Operations: Adding, Subtracting, Multiplying, and Dividing

Interactive video

•

6th - 10th Grade

10 questions

Exploring the Grinch's Christmas Heist

Interactive video

•

6th - 10th Grade

20 questions

Solving Systems of Equations

Quiz

•

8th - 10th Grade

Angle Sum/Difference Identities

20 questions

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$15\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$75\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$165\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$105\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$255\degree$

Use a sum or difference identity to find the EXACT value:

$\sin\left(15\degree\right)$

Use a sum or difference identity to find the EXACT value:
$\sin\left(75\degree\right)$

Use a sum or difference identity to find the EXACT value:
$\cos\left(75\degree\right)$

Use a sum or difference identity to find the EXACT value:

$\cos\left(105\degree\right)$

Use a sum or difference identity to find the EXACT value:

$\cos\left(\frac{\pi}{12}\right)$

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Angle Sum/Difference Identities

20 questions

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle: 15°15\degree15°

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle: 75°75\degree75°

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle: 165°165\degree165°

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle: 105°105\degree105°

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle: 255°255\degree255°

Use a sum or difference identity to find the EXACT value: sin⁡(15°)\sin\left(15\degree\right)sin(15°)

Use a sum or difference identity to find the EXACT value: sin⁡(75°)\sin\left(75\degree\right)sin(75°)

Use a sum or difference identity to find the EXACT value: cos⁡(75°)\cos\left(75\degree\right)cos(75°)

Use a sum or difference identity to find the EXACT value: cos⁡(105°)\cos\left(105\degree\right)cos(105°)

Use a sum or difference identity to find the EXACT value: cos⁡(π12)\cos\left(\frac{\pi}{12}\right)cos(12π​)

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$15\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$75\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$165\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$105\degree$

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$255\degree$

Use a sum or difference identity to find the EXACT value:

$\sin\left(15\degree\right)$

Use a sum or difference identity to find the EXACT value:
$\sin\left(75\degree\right)$

Use a sum or difference identity to find the EXACT value:
$\cos\left(75\degree\right)$

Use a sum or difference identity to find the EXACT value:

$\cos\left(105\degree\right)$

Use a sum or difference identity to find the EXACT value:

$\cos\left(\frac{\pi}{12}\right)$