Exam 4: Trigonometric Functions of Angles

Solve the given triangle. Round angles to one decimal place and side measures to 3 significant figures. b = 67 yd., c = 70.3 yd., $\beta$ = 70.0°

A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of $\theta$ drawn in standard position. If tan $\theta$ = , then what is cos $\theta$ ?

Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius 7/6 ft and arc length 8/7 ft.

Use the reciprocal identity To calculate csc 45°.

Find the complement of an angle that measures 72 degrees.

Peg and Meg live five miles apart. The school that they attend lies on a street that makes a 34° angle with the street connecting their houses when measured from Peg's house. The street connecting Meg's house and the school makes a 38° angle with the street connecting them. How far is it from Peg's house to the school?

Evaluate csc(-90°) + cos(360°).

Solve the given triangle and round to one decimal place. B = 57.0 cm., $\gamma$ = 61.8°, $\alpha$ = 63.4°

Use the triangle to write sec $\theta$ , if A = 60, B = 11, and C = 61.

Use the right triangle diagram below and the information given to find the indicated measure. α = 39°, c = 71 in, find b. Round your answer to two decimal places.

Evaluate cot(60° 53' 17"). Round answers to 3 decimal places.

Name the trigonometric function that has a value of

Convert 350 degrees to radians. Leave the answer in terms of $\pi$ .

The terminal side of an angle θ in standard position passes through the point (-2, -1). Calculate the value of sinθ. Round your answer to four decimal places.

Evaluate tan(-45°) exactly.

A hot air balloon is sighted at the same time by two friends who are 2.5 miles apart on the same side of the balloon. The angles of elevation from the two friends are 20.5° and 28°. How high is the balloon? Round to one decimal place.

Find the distance, s, a point travels along a circle over time t = 20 minutes, given the angular speed = 7 rotations per second and the radius r = 7 inches. Express your answer in miles (1 mile = 5,280 ft), and round your answer to one decimal place.

If sin θ = , and the terminal side of θ lies in quadrant IV, find tan θ.

Evaluate cot(-1410°) exactly.

Find the complement of an angle that measures 65 degrees.