cos ⁡ 7 5 o cos ⁡ 1 5 o − sin ⁡ 7 5 o sin ⁡ 1 5 o \cos75^o\cos15^o-\sin75^{o\ }\sin15^o cos 7 5 o cos 1 5 o − sin 7 5 o sin 1 5 o is equivalent to

cos ⁡ 9 0 o \cos\ 90^{o\ } cos 9 0 o

sin ⁡ 9 0 o \sin\ 90^{o\ } sin 9 0 o

sin ⁡ 6 0 o \sin\ 60^{o\ } sin 6 0 o

cos ⁡ 6 0 o \cos\ 60^{o\ } cos 6 0 o

Given sin ⁡ x = 3 5 a n d sin ⁡ y = 2 3 , \sin x=\frac{3}{5}and\ \sin y=\frac{2}{3}, sin x = 5 3 a n d sin y = 3 2 , where x a n d y x\ and\ y x a n d y are both in first quadrant. E v a l u a t e sin ⁡ ( x + y ) Evaluate\ \sin\left(x+y\right) E v a l u a t e sin ( x + y )

3 5 + 8 15 \frac{3\sqrt{5}+8}{15} 1 5 3 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"> + 8

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

2 5 + 12 15 \frac{2\sqrt{5}+12}{15} 1 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"> + 1 2

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

Trig Identities

Quiz

•

Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.TF.C.9, HSA.SSE.A.2, HSF.TF.C.8

+2

Standards-aligned

Dan Schwanekamp

Used 63+ times

FREE Resource

13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

csc x

tan x + 1

cot x

cot x + 1

Tags

CCSS.HSF.TF.C.9

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

secθ

cos²θ

sin²θ

sin²θ/cos²θ

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Simplify
(sec x)(cot x)(sin x)

sin x

- sin x

1

-1

Tags

CCSS.HSF.TF.C.8

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify: $\frac{1-\sin^2x}{\sec x}$

$\sin^2x$

$\cos^2x$

$\sin^3x$

$\cos^3x$

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify: $\sec x-\tan x\sin x$

$\sin x$

$\cos x$

$\csc x$

$\sec x$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.9

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

$\sin\ 90^{o\ }$

$\sin\ 60^{o\ }$

$\cos\ 90^{o\ }$

$\cos\ 60^{o\ }$

Tags

CCSS.HSF.TF.C.9

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use sum or difference angles identity to find the exact value for $\cos105^o$

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

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

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

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

Tags

CCSS.HSF.TF.C.9

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Trig Identities

13 questions

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

Simplify
(sec x)(cot x)(sin x)

Simplify: $\frac{1-\sin^2x}{\sec x}$

Simplify: $\sec x-\tan x\sin x$

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

Use sum or difference angles identity to find the exact value for $\cos105^o$

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

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

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Discover more resources for Mathematics

Trig Identities

13 questions

Simplify csc⁡ x(cos⁡x+sin⁡x)\csc\ x\left(\cos x+\sin x\right)csc x(cosx+sinx)

Simplify sin⁡θ(csc⁡θ−sin⁡θ)\sin\theta\left(\csc\theta-\sin\theta\right)sinθ(cscθ−sinθ)

Simplify (sec x)(cot x)(sin x)

Simplify: 1−sin⁡2xsec⁡x\frac{1-\sin^2x}{\sec x}secx1−sin2x​

Simplify: sec⁡x−tan⁡xsin⁡x\sec x-\tan x\sin xsecx−tanxsinx

cos⁡75ocos⁡15o−sin⁡75o sin⁡15o\cos75^o\cos15^o-\sin75^{o\ }\sin15^ocos75ocos15o−sin75o sin15o is equivalent to

Use sum or difference angles identity to find the exact value for cos⁡105o\cos105^ocos105o

Given sin⁡x=35and sin⁡y=23,\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},sinx=53​and siny=32​, where x and yx\ and\ yx and y are both in first quadrant. Evaluate sin⁡(x+y)Evaluate\ \sin\left(x+y\right)Evaluate sin(x+y)

Write the following expression as the sine, cosine, or tangent of an angle.cos(175)cos(55)+sin(175)sin(55)

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

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

Simplify

$\sin\theta\left(\csc\theta-\sin\theta\right)$

Simplify
(sec x)(cot x)(sin x)

Simplify: $\frac{1-\sin^2x}{\sec x}$

Simplify: $\sec x-\tan x\sin x$

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

Use sum or difference angles identity to find the exact value for $\cos105^o$

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

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