Exam 6: Analytic Trigonometry

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

Verify the identity .

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

The horizontal movement of a point that is k kilometers away from an earthquake's fault line can be estimated with Where M is the movement of the point in meters, f is the total horizontal displacement occurring along the fault line, k is the distance of the point from the fault line, and d is the depth in kilometers of the focal point of the earthquake. If an earthquake produced a displacement, f, of 2.8 meters and the depth of the focal point was 1.2 kilometers, then what is the movement, M , of a point that is 11.3 kilometers from the fault line? Round to 2 decimal places.

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

Write the expression in terms of x. If

Verify the trigonometric identity algebraically.

Verify the trigonometric identity .

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

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

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

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

Verify the identity

Use the cofunction identity to fill in the blank: cos 2° = sin____°.

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

Write sin (9x) cos (3x) - cos (9x) sin (3x) as a single trigonometric function.

Write as a product of sines and/or cosines.

Simplify Using half-angle identities. Do not evaluate.

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

The figure below shows the graph of Between -2 $\pi$ and 2 $\pi$ . The maximum and minimum values of the curve occur at the turning points and are found in the solutions of the equation Solve for the coordinates of the turning points of the curve between