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Problem 91
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. tan θ/2
Problem 93
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cot (θ + 180°)
Problem 95
Concept Check Suppose that 90° < θ < 180° . Find the sign of each function value. cos ( ―θ)
Problem 98
Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value. sec θ/2
Problem 101
Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value.
sec(―θ)
Problem 103
Concept Check Suppose that ―90° < θ < 90° . Find the sign of each function value. cos(θ―180°)
Problem 105
Concept Check Find a solution for each equation. tan (3θ ― 4°) = 1 / [cot(5θ ― 8°)]
Problem 107
Concept Check Find a solution for each equation. sin(4θ + 2°) csc(3θ + 5°) = 1
Problem 108
Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1
Problem 1
Give the measures of the complement and the supplement of an angle measuring 35° .
Problem 4
Find the angle of least positive measure that is coterminal with each angle. 792°
Problem 5
Solve each problem. Rotating Propeller The propeller of a speedboat rotates 650 times per min. Through how many degrees does a point on the edge of the propeller rotate in 2.4 sec?
Problem 6
Solve each problem. Rotating Pulley A pulley is rotating 320 times per min. Through how many degrees does a point on the edge of the pulley move in 2/3 sec?
Problem 7
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 119° 08' 03"
Problem 8
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"
Problem 9
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 275.1005°
Problem 11
Find the measure of each marked angle.
Problem 12
Find the measure of each marked angle.
Problem 13
Find the measure of each marked angle.
Problem 14
Find the measure of each marked angle.
Problem 15
Solve each problem. Length of a Road A camera is located on a satellite with its lens positioned at C in the figure. Length PC represents the distance from the lens to the film PQ, and BA represents a straight road on the ground. Use the measurements given in the figure to find the length of the road. (Data from Kastner, B., Space Mathematics, NASA.)
Problem 17
Find all unknown angle measures in each pair of similar triangles.
Problem 20
Find the unknown side lengths in each pair of similar triangles.
Problem 21
In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.
Problem 23
Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?
Problem 24
Find the six trigonometric function values for each angle. Rationalize denominators when applicable.
Problem 27
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (3 , ―4)
Problem 29
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (―8 , 15)
Problem 31
Find the values of the six trigonometric functions for an angle in standard position having each given point on its terminal side. Rationalize denominators when applicable. (6√3 , ―6)
Problem 35
An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . 12x + 5y = 0 , x ≥ 0 .