Exam 6: Analytic Trigonometry

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

Deer Population. The number of deer on an island is given by , where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 160.

Verify the trigonometric identity

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

Write cos 10x - cos 4x as a product of sines and/or cosines.

Write sin 4x - sin 2x as a product of sines and/or cosines.

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

A museum patron whose eye level is 6 feet above the floor is studying a painting that is 7 feet in height and mounted on the wall 3 feet above the floor. If the patron is x feet from the wall, θ is the angle that the patron's eye sweeps from the top to the bottom of the painting. Find the measure of the angle θ for x = 22. Round to the nearest degree).

Graph the function y = -5 cot x sec x tan x.

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

Use a half-angle identity to find csc if tan x = and . Give the exact answer.

Find the exact value of

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

The figure below shows the graph of between -2π and 2π. 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

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

Use a trigonometric substitution to simplify the expression so that it contains no radicals.

Verify the trigonometric identity (csc x - cot x)(sec x +1) = tan x algebraically.

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 ≤ θ ≤ 2π.

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