Trigonometry Applications (23 problems)

The following chart shows some common angles with their degrees and radian measures. Fill in the missing blanks by using the conversions between radians and degrees to find your solutions. Show all work to receive full credit.

Work shown here:

Solve the following equation

Solve the following trigonometric equations

Solve the following equation

Solve the following equation for

Find the solutions of the equation

on

Find the least positive anglesuch that

Solve the following equation

Prove the following trigonometric identity

An A-frame lake house is 21 feet wide. If the roof of the home makes a angle with the base of the home, what is the length of the house from ground level to the peak of the roof? Round final answer to the nearest foot.

Use common trigonometric identities for the functions given to find the indicated trigonometric functions. (Hint: Remember the reciprocal properties of sine, cosine, and tangent.) Show all work to receive full credit. Give answers in exact form – no decimals.

A. If and , what are the values of

a)

b) =

c) =

B. If and , what are the values of

a) =

b) =

c) =

Prove the following identity

Using trigonometric properties, show that