Use a sum or difference formula to find an exact value of sin ⁡ ( 7 π 12 ) \sin\left(\frac{7\pi}{12}\right) sin ( 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">

3 2 \frac{\sqrt{3}}{2} 2 3 <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">

2 − 3 2-\sqrt{3} 2 − 3 <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">

If cos θ = 4/5 and 3 π 2 < θ < 2 π \frac{3\pi}{2}<\theta<2\pi 2 3 π < θ < 2 π Find sin 2θ

− 24 25 -\frac{24}{25} − 2 5 2 4

− 25 24 -\frac{25}{24} − 2 4 2 5

Find the exact value of sin ⁡ 2 x \sin2x sin 2 x if sin ⁡ x = 12 13 \sin x=\frac{12}{13} sin x = 1 3 1 2 and x is in the first quadrant.

120 169 \frac{120}{169} 1 6 9 1 2 0

25 169 \frac{25}{169} 1 6 9 2 5

60 169 \frac{60}{169} 1 6 9 6 0

If sin ⁡ A = 3 5 , sin ⁡ B = 2 3 , \sin A=\frac{3}{5},\sin B=\frac{2}{3}, sin A = 5 3 , sin B = 3 2 , a n d ∠ A a n d ∠ B and\ \angle A\ and\ \angle B a n d ∠ A a n d ∠ B are in the first quadrant, what is the value of cos ⁡ ( A − B ) ? \cos\left(A-B\right)? cos ( A − B ) ?

4 5 + 6 15 \frac{4\sqrt{5}+6}{15} 1 5 4 5 <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

4 5 − 6 15 \frac{4\sqrt{5}-6}{15} 1 5 4 5 <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

4 5 + 2 5 \frac{4\sqrt{5}+2}{5} 5 4 5 <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

If sin ⁡ A = 4 5 , tan ⁡ B = 5 12 , \sin A=\frac{4}{5},\tan B=\frac{5}{12}, sin A = 5 4 , tan B = 1 2 5 , and A and B are first quadrant angles, what is the value of sin ⁡ ( A + B ) \sin\left(A+B\right) sin ( A + B ) ?

− 33 65 -\frac{33}{65} − 6 5 3 3

− 63 65 -\frac{63}{65} − 6 5 6 3

Use sum or difference angles identity to find the exact value for sin ⁡ ( − π 12 ) \sin\ \left(\frac{-\pi}{12}\right) sin ( 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">

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">

− 3 2 -\frac{\sqrt{3}}{2} − 2 3 <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">

Trig Formulas (Sum/Difference & Double Angle)

Authored by Sarah Dragoon

Mathematics

9th - 12th Grade

CCSS covered

Used 44+ times

Trig Formulas (Sum/Difference & Double Angle)

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11 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value of the expression.
$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$

$\frac{1}{2}$

$-\frac{1}{2}$

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

$-\frac{\sqrt{3}}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Use a sum or difference formula to find an exact value of $\sin\left(\frac{7\pi}{12}\right)$

$\frac{\sqrt{3}}{2}$

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

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

$2-\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If cos θ = 4/5 and $\frac{3\pi}{2}<\theta<2\pi$
Find sin 2θ

$-\frac{1}{5}$

$\frac{24}{25}$

$-\frac{24}{25}$

$-\frac{25}{24}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the exact value of $\sin2x$ if $\sin x=\frac{12}{13}$ and x is in the first quadrant.

$\frac{120}{169}$

$\frac{25}{169}$

$\frac{60}{169}$

$\frac{5}{13}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are in the first quadrant, what is the value of $\cos\left(A-B\right)?$

$-\frac{2}{3}$

$\frac{4\sqrt{5}-6}{15}$

$\frac{4\sqrt{5}+2}{5}$

$\frac{4\sqrt{5}+6}{15}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

$\frac{63}{65}$

$-\frac{33}{65}$

$\frac{33}{65}$

$-\frac{63}{65}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If $\sin\theta=\frac{\sqrt{5}}{3}$ and $\frac{\pi}{2}<\theta<\pi$ , then $\cos2\theta$ equals

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{1}{9}$

$-\frac{1}{9}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Use sum or difference angles identity to find the exact value for $\sin\ \left(\frac{-\pi}{12}\right)$

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

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

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

$-\frac{\sqrt{3}}{2}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the exact value of $\sin2\theta$ if $\sin\theta=\frac{12}{13}$ and $\theta$ is in the first quadrant.

120/169

25/169

60/169

5/13

Tags

CCSS.HSF.TF.C.9

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If cos θ = 4/5 and $\frac{3\pi}{2}<\theta<2\pi$ , find sin 2θ

-1/5

24/25

-24/25

-25/24

Tags

CCSS.HSF.TF.C.9

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Trig Formulas (Sum/Difference & Double Angle)

Find the exact value of the expression. sin⁡(5π12)cos⁡(π4)−cos⁡(5π12)sin⁡(π4)\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)sin(125π​)cos(4π​)−cos(125π​)sin(4π​)

Use a sum or difference formula to find an exact value of sin⁡(7π12)\sin\left(\frac{7\pi}{12}\right)sin(127π​)

If cos θ = 4/5 and 3π2<θ<2π\frac{3\pi}{2}<\theta<2\pi23π​<θ<2π Find sin 2θ

Find the exact value of sin⁡2x\sin2xsin2x if sin⁡x=1213\sin x=\frac{12}{13}sinx=1312​ and x is in the first quadrant.

If sin⁡A=35,sin⁡B=23,\sin A=\frac{3}{5},\sin B=\frac{2}{3},sinA=53​,sinB=32​, and ∠A and ∠Band\ \angle A\ and\ \angle Band ∠A and ∠B are in the first quadrant, what is the value of cos⁡(A−B)?\cos\left(A-B\right)?cos(A−B)?

If sin⁡A=45,tan⁡B=512,\sin A=\frac{4}{5},\tan B=\frac{5}{12},sinA=54​,tanB=125​, and A and B are first quadrant angles, what is the value of sin⁡(A+B)\sin\left(A+B\right)sin(A+B) ?

If sin⁡θ=53\sin\theta=\frac{\sqrt{5}}{3}sinθ=35​​ and π2<θ<π\frac{\pi}{2}<\theta<\pi2π​<θ<π , then cos⁡2θ\cos2\thetacos2θ equals

Use sum or difference angles identity to find the exact value for sin⁡ (−π12)\sin\ \left(\frac{-\pi}{12}\right)sin (12−π​)

Find the exact value of sin⁡2θ\sin2\thetasin2θ if sin⁡θ=1213\sin\theta=\frac{12}{13}sinθ=1312​ and θ\thetaθ is in the first quadrant.

If cos θ = 4/5 and 3π2<θ<2π\frac{3\pi}{2}<\theta<2\pi23π​<θ<2π , find sin 2θ

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If cos θ = 4/5 and $\frac{3\pi}{2}<\theta<2\pi$
Find sin 2θ

Find the exact value of $\sin2x$ if $\sin x=\frac{12}{13}$ and x is in the first quadrant.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are in the first quadrant, what is the value of $\cos\left(A-B\right)?$

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Find the exact value of $\sin2\theta$ if $\sin\theta=\frac{12}{13}$ and $\theta$ is in the first quadrant.

If cos θ = 4/5 and $\frac{3\pi}{2}<\theta<2\pi$ , find sin 2θ