Chapter 9

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 90^{\circ} $$

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ -400^{\circ} $$

The bed of a truck is 5 feet above the ground. The driver of the truck uses a ramp 13 feet long to load and unload the truck. Find the sine, cosine, and tangent values of the angle that the ramp makes with the ground.

In \(3-44,\) find the exact value. $$ \sin 45^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(-130^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \cos 485^{\circ} $$

In \(11-18, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\csc \theta\) c. \(\sec \theta\) d. \(\cot \theta\) \((-4,8)\)

In \(13-20, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) $$ (-3,-4) $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ -180^{\circ} $$

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 750^{\circ} $$

A 20-meter line is used to keep a weather balloon in place. The sine of the angle that the line makes with the ground is \(\frac{3}{4}\) . How high is the balloon in the air?

In \(3-44,\) find the exact value. $$ \csc 45^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(505^{\circ}\)

In \(11-18, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\csc \theta\) c. \(\sec \theta\) d. \(\cot \theta\) \((9,-9)\)

In \(13-20, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) $$ (-3,6) $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 81^{\circ} $$

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 1,050^{\circ} $$

From a point on the ground that is 100 feet from the base of a building, the tangent of the angle of elevation of the top of the building is \(\frac{5}{4} .\) To the nearest foot, how tall is the building?

In \(3-44,\) find the exact value. $$ \tan 45^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\sin 215^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin \left(-10^{\circ}\right) $$

In \(13-20, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) $$ (-2,6) $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 137^{\circ} $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ 390^{\circ} $$

From the top of a lighthouse 75 feet high, the cosine of the angle of depression of a boat out at sea is \(\frac{4}{5} .\) To the nearest foot, how far is the boat from the base of the lighthouse?

In \(3-44,\) find the exact value. $$ \cot 45^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\cos 95^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 350^{\circ} $$

If \(\sin \theta=0,\) find all possible values of: a. \(\cos \theta\) b. \(\tan \theta \quad\) c. \(\sec \theta\)

In \(13-20, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) $$ (4,-4) $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 229^{\circ} $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ 412^{\circ} $$

In \(3-44,\) find the exact value. $$ \cos 180^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\tan 255^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 190^{\circ} $$

In \(13-20, P\) is a point on the terminal side of an angle in standard position with measure \(\theta\) and on a circle with center at the origin and radius \(r .\) For each point \(P,\) find: a. \(r\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) $$ (9,-3) $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 312^{\circ} $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ 1,000^{\circ} $$

In \(3-44,\) find the exact value. $$ \sec 180^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\cos 312^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \cos 18^{\circ} 12^{\prime} $$

If \(\tan \theta\) is undefined, find all possible values of: \(\mathbf{a} . \cos \theta \quad \mathbf{b} . \sin \theta \quad \mathbf{c} . \cot \theta\)

In \(21-26,\) if \(\theta\) is the measure of \(\angle A O B,\) an angle in standard position, name the quadrant in which the terminal side of \(\angle A O B\) lies. $$ \sin \theta>0, \cos \theta>0 $$

In \(15-22\) , for each given angle in standard position, determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle. $$ 540^{\circ} $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ -10^{\circ} $$

In \(3-44,\) find the exact value. $$ \sin 180^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\tan 170^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 57^{\circ} 40^{\prime} $$

If \(\sec \theta\) is undefined, find all possible values of \(\sin \theta\)

In \(21-26,\) if \(\theta\) is the measure of \(\angle A O B,\) an angle in standard position, name the quadrant in which the terminal side of \(\angle A O B\) lies. $$ \sin \theta<0, \cos \theta>0 $$