Exam 6: Analytic Trigonometry

Write sin (10x) cos (8x) - cos (10x) sin (8x) as a single trigonometric function.

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

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

Verify the identity .

Use a half-angle identity to find the exact value of tan 345°.

Evaluate exactly, if possible.

Graph by first rewriting as a sine or cosine of a difference or sum.

The number of hours of daylight in San Diego, California, can be modeled with H(t) =12 + 2.4sin(0.017t - 1.377) where t is the day of the year (January 1, t = 1 etc) For what value of t is the number of hours equal to 11.7? If May 31 is the 151st day of the year, what month and day correspond to that value of t? Round to 2 decimal places. The day of the year is _________

Use a reciprocal identity to find cos θ if sec θ = .

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

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

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

Find the exact value of tan(210°).

Use a half-angle identity to find csc if tan x = and . Give the exact answer. Do not rationalize the denominator.

Solve the given trigonometric equation exactly for all reals.

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 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.

Find the exact value of if the terminal side of Lies in I and the terminal side of lies in IV.

Write sin1.2x + sin0.4x as a product of sines and/or cosines.

If csc x = And cos x > 0, find cos2x.