S o l v e 4 cos ⁡ x + 3 = 5 f o r 0 ≤ x < 360 ° Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree S o l v e 4 cos x + 3 = 5 f o r 0 ≤ x < 3 6 0 °

x = 60 ° , 300 ° x\ =\ 60\degree,\ 300\degree x = 6 0 ° , 3 0 0 °

x = 60 ° , 120 ° x\ =\ 60\degree,\ 120\degree x = 6 0 ° , 1 2 0 °

x = 30 ° , 150 ° x\ =\ 30\degree,\ 150\degree x = 3 0 ° , 1 5 0 °

x = 30 ° , 330 ° x\ =\ 30\degree,\ 330\degree x = 3 0 ° , 3 3 0 °

S o l v e tan ⁡ x + 3 = 0 f o r 0 ≤ x < 360 ° Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree S o l v e tan x + 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"> = 0 f o r 0 ≤ x < 3 6 0 °

120 ° , 300 ° 120\degree,\ 300\degree 1 2 0 ° , 3 0 0 °

30 ° , 210 ° 30\degree,\ 210\degree 3 0 ° , 2 1 0 °

150 ° , 330 ° 150\degree,\ 330\degree 1 5 0 ° , 3 3 0 °

60 ° , 240 ° 60\degree,\ 240\degree 6 0 ° , 2 4 0 °

S o l v e 3 cot ⁡ x + 5 = 8 f o r 0 ≤ x < 2 π Solve\ 3\cot x\ +\ 5\ =\ 8\ \ for\ \ 0\ \le\ x\ <\ 2\pi S o l v e 3 cot x + 5 = 8 f o r 0 ≤ x < 2 π

π 4 , 5 π 4 \frac{\pi}{4},\ \frac{5\pi}{4} 4 π , 4 5 π

π 2 , 3 π 2 \frac{\pi}{2},\ \frac{3\pi}{2} 2 π , 2 3 π

3 π 4 , 7 π 4 \frac{3\pi}{4},\ \frac{7\pi}{4} 4 3 π , 4 7 π

S o l v e 6 + 4 csc ⁡ x = 14 f o r 0 ≤ x < 2 π Solve\ \ 6\ +\ 4\csc x\ =\ 14\ \ for\ \ 0\le\ x\ <\ 2\pi S o l v e 6 + 4 csc x = 1 4 f o r 0 ≤ x < 2 π

π 6 , 5 π 6 \frac{\pi}{6},\ \frac{5\pi}{6} 6 π , 6 5 π

π 3 , 2 π 3 \frac{\pi}{3},\ \frac{2\pi}{3} 3 π , 3 2 π

4 π 3 , 5 π 3 \frac{4\pi}{3},\ \frac{5\pi}{3} 3 4 π , 3 5 π

7 π 6 , 11 π 6 \frac{7\pi}{6},\ \frac{11\pi}{6} 6 7 π , 6 1 1 π

Which of the following is the same as cos ⁡ ( A + B ) \cos\ \left(A+B\right) cos ( A + B )

cos ⁡ A cos ⁡ B − sin ⁡ A sin ⁡ B \cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B cos A cos B − sin A sin B

sin ⁡ A cos ⁡ B + cos ⁡ A sin ⁡ B \sin A\cos\ B\ +\ \cos\ A\ \sin\ B sin A cos B + cos A sin B

sin ⁡ A cos ⁡ B − cos ⁡ A sin ⁡ B \sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B sin A cos B − cos A sin B

cos ⁡ A cos ⁡ B + sin ⁡ A sin ⁡ B \cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B cos A cos B + sin A sin B

Which of the following is equivalent to tan ⁡ ( A − B ) \tan\ \left(A-B\right) tan ( A − B )

tan ⁡ A − tan ⁡ B 1 + tan ⁡ A tan ⁡ B \frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B} 1 + tan A tan B tan A − tan B

tan ⁡ A − tan ⁡ B \tan\ A\ -\ \tan\ B tan A − tan B

tan ⁡ A + tan ⁡ B 1 − tan ⁡ A tan ⁡ B \frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B} 1 − tan A tan B tan A + tan B

sin ⁡ A cos ⁡ B \frac{\sin\ A}{\cos\ B} cos B sin A

Expand cos ⁡ ( π 5 + π 6 ) \cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right) cos ( 5 π + 6 π )

cos ⁡ π 5 cos ⁡ π 6 − sin ⁡ π 5 sin ⁡ π 6 \cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\ cos 5 π cos 6 π − sin 5 π sin 6 π

cos ⁡ π 5 cos ⁡ π 6 + sin ⁡ π 5 sin ⁡ π 6 \cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\ cos 5 π cos 6 π + sin 5 π sin 6 π

cos ⁡ 2 π 11 \cos\ \frac{2\pi}{11} cos 1 1 2 π

cos ⁡ π 5 sin ⁡ π 6 − cos ⁡ π 5 sin ⁡ π 6 \cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\ cos 5 π sin 6 π − cos 5 π sin 6 π

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

tan ⁡ 4 5 o + tan ⁡ 3 0 o 1 − tan ⁡ 4 5 o tan ⁡ 3 0 o \frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o} 1 − tan 4 5 o tan 3 0 o tan 4 5 o + tan 3 0 o is equivalent to

tan ⁡ 7 5 o \tan75^o tan 7 5 o

tan ⁡ 1 5 o \tan\ 15^o tan 1 5 o

sin ⁡ 4 5 o cos ⁡ 3 0 o \frac{\sin45^o}{\cos30^o} cos 3 0 o sin 4 5 o

tan ⁡ 9 0 o \tan90^{o\ } tan 9 0 o

Use sum or difference angles identity to find the exact value for cos ⁡ 10 5 o \cos105^o cos 1 0 5 o

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">

− 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">

Trig Identities Test Review

Authored by Edward Garcia

Mathematics

11th Grade

CCSS covered

Used 4+ times

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30 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\frac{\sin\ x}{\cos\ x}\ =\ ?$

csc x

sec x

tan x

cot x

$\frac{1}{\cos\ x}\ =\ ?$

csc x

sec x

tan x

cot x

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\left(\sin\ x\right)\left(\cot\ x\right)\ =\ ?$

cos x

sin x

csc x

sec x

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\cos^2x\ +\ \sin^2x\ =\ ?$

tan x

cot x

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\left(\sin\ x\right)\left(\csc\ x\right)\ =\ ?$

cos x

cot x

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify: $\secθ\sinθ$

cos θ

csc θ

tan θ

cot θ

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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

$\sin x$

$\cos x$

$\csc x$

$\sec x$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

$\cot^2x$

$\tan^2x$

$\csc^2x$

$\sec^2x$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\frac{\cos x}{1+\sin x}+\tan x$

$\csc x$

$\sec x$

$\cot x$

$1$

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Simplify: $\left(\cos\ θ\right)\left(\sec\ θ-\cosθ\right)$

$\sin^2θ$

$\cos^2θ$

$\csc^2\theta$

$\sec^2\theta$

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Trig Identities Test Review

sin⁡ xcos⁡ x = ?\frac{\sin\ x}{\cos\ x}\ =\ ?cos xsin x​ = ?

1cos⁡ x = ?\frac{1}{\cos\ x}\ =\ ?cos x1​ = ?

(sin⁡ x)(cot⁡ x) = ?\left(\sin\ x\right)\left(\cot\ x\right)\ =\ ?(sin x)(cot x) = ?

cos⁡2x + sin⁡2x = ?\cos^2x\ +\ \sin^2x\ =\ ?cos2x + sin2x = ?

(sin⁡ x)(csc⁡ x) = ?\left(\sin\ x\right)\left(\csc\ x\right)\ =\ ?(sin x)(csc x) = ?

Simplify: sec⁡θsin⁡θ\secθ\sinθsecθsinθ

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

Simplify: sin⁡2x+cos⁡2x+cot⁡2x1+tan⁡2x\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}1+tan2xsin2x+cos2x+cot2x​

cos⁡x1+sin⁡x+tan⁡x\frac{\cos x}{1+\sin x}+\tan x1+sinxcosx​+tanx

Simplify: (cos⁡ θ)(sec⁡ θ−cos⁡θ)\left(\cos\ θ\right)\left(\sec\ θ-\cosθ\right)(cos θ)(sec θ−cosθ)

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$\frac{\sin\ x}{\cos\ x}\ =\ ?$

$\frac{1}{\cos\ x}\ =\ ?$

$\left(\sin\ x\right)\left(\cot\ x\right)\ =\ ?$

$\cos^2x\ +\ \sin^2x\ =\ ?$

$\left(\sin\ x\right)\left(\csc\ x\right)\ =\ ?$

Simplify: $\secθ\sinθ$

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

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

$\frac{\cos x}{1+\sin x}+\tan x$

Simplify: $\left(\cos\ θ\right)\left(\sec\ θ-\cosθ\right)$