(MATH Analysis ONLY) Chapter 5 exam

4

Find the equation of a circle with a center of (1,2) and a radius of \sqrt{17}.

_______ 

What are the x-intercepts of the circle?

_______  _______ 

What are the y-intercepts of the circle?

_______  _______

4

On a circle of radius 8 cm, find the following

a. Length of the arc that subtends a central angle of 135\degree? 

_______ 
b. Area of a sector with a central angle of 135\degree?

_______ 

4

If \theta=\frac{5\pi}{3}, what are the exact values of the following: 

\sin(\theta)=_______
\cos(\theta)=_______  
\tan(\theta)=_______ 
\csc(\theta)=_______ 
\sec(\theta)=_______ 
\cot(\theta)=_______ 

4

If \cos(\theta)=\frac{4}{15} and \theta is in the fourth quadrant, calculate the following.

\sin(\theta)=_______ 
\tan(\theta)=_______ 
\csc(\theta)=_______ 
\sec(\theta)=_______ 
\cot(\theta)=_______ 

4

Prove the equation below is true

\frac{\tan^{2}(\theta)\cdot \cot(\theta)}{\cos(\theta)}=(1+\tan^{2}(\theta))\cdot \sin(\theta)

4

Solve for x

4

Kelly is flying a kite to which the angle of elevation is 70˚ and the hand that is holding the kite is 4 feet above the ground. The string on the kite is 65 meters long. How far is the kite above the ground?

Prove the equation below is true\frac{\tan^{2}(\theta)\cdot \cot(\theta)}{\cos(\theta)}=(1+\tan^{2}(\theta))\cdot \sin(\theta)

Solve for x

Kelly is flying a kite to which the angle of elevation is 70˚ and the hand that is holding the kite is 4 feet above the ground. The string on the kite is 65 meters long. How far is the kite above the ground?

Prove the equation below is true

\frac{\tan^{2}(\theta)\cdot \cot(\theta)}{\cos(\theta)}=(1+\tan^{2}(\theta))\cdot \sin(\theta)