Precalculus 5.1-5.3 Quiz

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

Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin ² x (1 + cot ² x)

• cot x

• 1

• sin x

• cos x

Simplify the following trigonometric expression:
 $\frac{\sec^2x\ -1}{\sec^2x}$  

•  $\sec^2x$  

• 1

•   $\sin\ x$  

•  $\sin^2x$  

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

When verifying the identity  $\left(\tan^2x+1\right)\left(\cos^2x-1\right)=-\tan^2x$  
The first step would be:
 $\left(\sec^2x\right)\left(-\sin^2x\right)$  
The reason for this step is

• Pythagorean Identities

• Adding

• Multiplying

• Reciprocal Identities

 $\sec\ x\ -\ 2=0$  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

 Solve the multiple-angle equation.
 $\cos\ \frac{x}{2}=-\frac{\sqrt{3}}{2}$  

•  $x=\frac{5\pi}{3}+4\pi n\ and$  
  
   $\ x=\frac{7\pi}{3}+4\pi n$  
  

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

•  $x=\frac{5\pi}{6}+2\pi n\ and\$  
  
   $x=\frac{7\pi}{6}+2\pi n$  
  

•  $x=\frac{7\pi}{6}+2\pi n\ and$  
  
   $\ x=\frac{11\pi}{6}+2\pi n$  
  

•  $x=\frac{5\pi}{3}+2\pi n\ and$  
  
   $\ x=\frac{8\pi}{3}+2\pi n$