PreCalculus Trigonometric Identities

Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x

• cot x

• 1

• sin x

• cos x

Tags

CCSS.HSF.TF.C.8

Simplify the following trigonometric expression as much as possible:

sin B + cos B cot B

• cos B

• cot B

• sin B

• csc B

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the following trigonometric expression:  $\frac{\sin x\ \csc\ x}{\cot x}$  

•  $\tan\ x$  

•  $\cot\ x$  

• 1

•  $\cos\ x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

When verifying the identity:  $\left(1-\sin x\right)\left(1+\sin x\right)=\cos^2x$  
The first step would be to

• Add

• Subtract

• Substitute

• Multiply 

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\sec\ x\ -\ 2=0$  Which of the following is a solution to the given equation?

•  $x=\frac{\pi}{4}$  

•  $x=\frac{5\pi}{6}$  

•  $x=\frac{7\pi}{4}$  

•  $x=\frac{5\pi}{3}$  

•  $x=\frac{7\pi}{6}$  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

Solve the following equation, for all real numbers. 
 $\sin^2x+\sin x\ =0$  

•  $x=n\pi\ \ and\ \$  
  
   $x=\frac{3\pi}{4}+n\pi$  
  

•  $x=n\pi\ \ and\$  
  
   $\ x=\frac{3\pi}{2}+n\pi$  
  

•  $x=n\pi\ \ and\$  
  
   $\ x=\frac{\pi}{2}+n\pi$  
  

•   $x=n\pi\ \ and\$  
  
   $\ x=\frac{3\pi}{2}+2n\pi$  
  

•  $x=\frac{2\pi}{3}+2n\pi\ \ and\$  
  
   $\ x=\frac{5\pi}{3}+2n\pi$  
  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.2

cot(90⁰-θ) is equivalent to ?

• tanθ
• sinθ
• cosθ
• secθ

Tags

CCSS.HSG.SRT.C.7

Solve on the Interval [0,2π)

tan(x)+1=2

• 0 and π

• 3π/4 and 7π/4

• π/4 and 5π/4

• 3π/4 and 5π/4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

Which of these is NOT
 a solution to
tan θ = 0 ?

• θ = 0
• θ = π /2
• θ = π
• θ = 2π

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.C.8

Why doesn't 2cosx − 3 = 0 have solutions?

• cosx is never bigger than one

• cosx is never equal to a fraction

• Actually, this equation does have a solution, x = π

• This equation will have a solution tomorrow.

Tags

CCSS.HSF.IF.B.5