Given sin ⁡ α = − 3 5 , cos ⁡ α = − 4 5 \sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5} sin α = − 5 3 , cos α = − 5 4 and cos ⁡ β = 2 5 5 , sin ⁡ β = − 5 5 \cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5} cos β = 5 2 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"> , sin β = − 5 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"> Find the exact value of sin (α+β):

− 2 5 25 -\frac{2\sqrt{5}}{25} − 2 5 2 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 − 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">

8 4 \frac{\sqrt{8}}{4} 4 8 <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">

Find the exact value. cos ⁡ ( 265 ° − 25 ° ) \cos\left(265\degree-25\degree\right) cos ( 2 6 5 ° − 2 5 ° )

− 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">

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">

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

Sum/Difference & Double Angle Formulas

Authored by Elizabeth Anderson

Mathematics

10th - 12th Grade

CCSS covered

Used 200+ times

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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

3 mins • 1 pt

Given $\sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5}$ and $\cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5}$
Find the exact value of sin (α+β):

$-\frac{2\sqrt{5}}{25}$

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

$\frac{\sqrt{8}}{4}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Given tan α = 3/4 and tan β = (-1/2)
Please find the sum and difference:
tan (α-β)=

$-\frac{10\sqrt{5}}{25}$

$-\frac{2\sqrt{5}}{25}$

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

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the exact value.
$\cos\left(265\degree-25\degree\right)$

$\frac{53}{12}$

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

$-\frac{1}{2}$

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

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Use a sum or difference formula to find an exact value of sin 105º

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

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

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

$2-\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Please select the correct solution
cos²x + sin ²x=
^{(It's on your reference sheet!!)}

csc²x + sec²x

sin²x

1 - sin²x

Tags

CCSS.HSF.TF.C.8

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

$-\frac{1}{5}$

$\frac{24}{25}$

$-\frac{24}{25}$

$-\frac{25}{24}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

3 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

3 mins • 1 pt

sin2u =

$\sin u\cos u$

$2\sin u\cos u$

$\sin^2u$

$2\sin^2u$

Tags

CCSS.HSF.TF.C.9

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

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

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{1}{9}$

$-\frac{1}{9}$

Tags

CCSS.HSF.TF.C.9

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Sum/Difference & Double Angle Formulas

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​)

Given sin⁡α=−35, cos⁡α=−45\sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5}sinα=−53​, cosα=−54​ and cos⁡β=255, sin⁡β=−55\cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5}cosβ=525​​, sinβ=−55​​ Find the exact value of sin (α+β):

Given tan α = 3/4 and tan β = (-1/2)Please find the sum and difference: tan (α-β)=

Find the exact value. cos⁡(265°−25°)\cos\left(265\degree-25\degree\right)cos(265°−25°)

Use a sum or difference formula to find an exact value of sin 105º

Please select the correct solution cos 2 x + sin 2 x= (It's on your reference sheet!!)

Use a double-angle identity to find the exact value of each expressioncos θ = 4/5 and 270° < θ < 360°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.

sin2u =

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

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

Given $\sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5}$ and $\cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5}$
Find the exact value of sin (α+β):

Given tan α = 3/4 and tan β = (-1/2)
Please find the sum and difference:
tan (α-β)=

Find the exact value.
$\cos\left(265\degree-25\degree\right)$

Please select the correct solution
cos²x + sin ²x=
^{(It's on your reference sheet!!)}

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

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

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