Solve the problem.
1) A pendulum swings through an angle of 15° each second. If the pendulum is 20 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places.
2) A radio transmission tower is 250 feet tall. How long should a guy wire be if it is to be attached 25 feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest tenth of a foot.
3) A straight trail with a uniform inclination of 12° leads from a lodge at an elevation of 545 feet to a mountain lake at an elevation of 6400 feet. What is the length of the trail (to the nearest foot)?
Use identities to find the indicated value. Where necessary, rationalize denominators.
4) sin t = , cos t = Find csc t.
Use the given triangles to evaluate the expressions. Rationalize all denominators.
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5) cos 60°
6) tan 135°
7) sin 150°
Verify the identity.
8)
Use the given information to find the exact value of the expression.
9) tan θ = 13/12, θ lies in quadrant III Find sin 2θ.
Use the given information to find the exact value of the trigonometric function.
10) csc θ = 3, θ lies in quadrant I Find .
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