Exam 6: Analytic Trigonometry

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Verify the trigonometric identity algebraically.

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

Find the exact value of if the terminal side of lies in QII and the terminal side of lies in QIV.

Verify the identity

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

Use a calculator to evaluate the expression. Give answer in degrees and round to two decimal places.

Write sin 10x + sin 2 x as a product of sines and/or cosines.

Use fundamental identities to simplify

Functions. Consider a 13-foot ladder placed against a wall such that the distance from the top of the ladder to the floor is h feet and the angle between the floor and the ladder is θ. a. Write the height, h, as a function of angle θ. b. If the ladder is pushed toward the wall, increasing the angle θ by 13°, write a new function for the height as the height as a function of θ + 13° and then express in terms of sines and cosines of θ + 13°. Give the exact answer.

Use fundamental identities to simplify sin x csc x - sin² x.

Evaluate the expression exactly if possible. If not possible, state why.

If cot x = and x is in QIV, find csc 2x.

Write sin 8x sin 5x as a sum or difference of sines and/or cosines.

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

Simplify using half-angle identities. Do not evaluate.

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Solve the given trigonometric equation exactly over the interval, 0 $\le$$\theta$$\le$ 2 $\pi$ .

Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.