Practice: Trigonometric Identities

Which of the following is NOT a Pythagorean identity?

• $\tan^2x+1=\sec^2x$

• $\cos2x\ =\ \cos^2x-\sin^2x$

• $\sin^2x\ +\ \cos^2x=1$

• $1+\cot^2x\ =\ \csc^2x$

Tags

CCSS.HSF.TF.C.8

Simplify:  $\cot x\sin x\sec^2x$ 

•  $\cos x$  

•  $\tan x$  

•  $\csc x$  

•  $\sec x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify:  $\cos x-\cos x\sin^2x$  

•  $\sin^3x$  

•  $\cos^3x$  

•  $\tan x\sec^2x$  

•  $1$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.9

Which of the following is false?

• $\sin\left(-x\right)=-\sin\left(x\right)$

• $\cos\left(-x\right)=-\cos\left(x\right)$

• $\tan\left(-x\right)=-\tan\left(x\right)$

• $\cot\left(-x\right)=-\cot\left(x\right)$

Tags

CCSS.HSF.TF.A.4

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

•  $\frac{1-\cos x}{\sin x}$  

•  $0$  

•  $-\cos x$  

•  $\csc x-1$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Simplify:  $\frac{1}{1-\tan x}-\frac{1}{1+\tan x}$ 

•  $\tan2x$  

•  $\tan^2x$  

•  $-\tan x$  

•  $\tan x+\tan^22x$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.9

Which expression is equivalent to the trigonometric expression  $\frac{\cos^2\left(\theta\right)-1}{\sin^2\left(\theta\right)-1}$  ?

•  $\cot^{2\ }\left(\theta\right)$  

•  $\tan^{2\ }\left(\theta\right)$  

•  $-\cot^{2\ }\left(\theta\right)$  

•  $-\tan^{2\ }\left(\theta\right)$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which expression is equivalent to the trigonometric expression  $\frac{\sin^2\left(\theta\right)+\cos^2\left(\theta\right)}{\sin\left(\theta\right)}$  ?

•  $\sec\left(\theta\right)$  

•  $1$  

•  $\csc\left(\theta\right)$  

•  $\csc^2\left(\theta\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

Which expression is equivalent to the trigonometric expression  $\frac{\tan\left(\theta\right)+\cot\left(\theta\right)}{\cot\left(\theta\right)}$  ?

•  $\sec\left(\theta\right)$  

•  $\sec^2\left(\theta\right)$  

•  $\cot\left(\theta\right)$  

•  $\tan^2\left(\theta\right)$  

Which expression is equivalent to the trigonometric expression  $\csc^2\left(\theta\right)-\cot^2\left(\theta\right)+\tan^2\left(\theta\right)$  ?

•  $\sec^2\left(\theta\right)$  

•  $\sec\left(\theta\right)$  

•  $\csc\left(\theta\right)$  

•  $\csc^2\left(\theta\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8