Chapter 9

In \(3-38,\) find each function value to four decimal places. $$ \tan 200^{\circ} $$

In \(3-10,\) the terminal side of \(\angle R O P\) in standard position intersects the unit circle at \(P .\) If \(\mathrm{m} \angle R O P\) is \(\theta,\) find: a. \(\sin \theta\) b. \(\cos \theta\) c.tan \(\theta\) d. \(\sec \theta\) e. \(\csc \theta\) f. \(\cot \theta\) $$ \left(-\frac{\sqrt{5}}{3},-\frac{2}{3}\right) $$

In \(3-11, P\) is the point at which the terminal side of an angle in standard position intersects the unit circle. The measure of the angle is \(\theta .\) For each point \(P\) the \(x\) -coordinate and the quadrant is given. Find: a. the \(y\) -coordinate of \(P\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) \(\left(\frac{\sqrt{5}}{3}, y\right),\) first quadrant

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 25^{\circ} $$

In \(3-44,\) find the exact value. $$ \sec 60^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(175^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 20^{\circ} $$

In \(3-10,\) the terminal side of \(\angle R O P\) in standard position intersects the unit circle at \(P .\) If \(\mathrm{m} \angle R O P\) is \(\theta,\) find: a. \(\sin \theta\) b. \(\cos \theta\) c.tan \(\theta\) d. \(\sec \theta\) e. \(\csc \theta\) f. \(\cot \theta\) $$ \left(-\frac{\sqrt{7}}{5}, \frac{3 \sqrt{2}}{5}\right) $$

In \(3-11, P\) is the point at which the terminal side of an angle in standard position intersects the unit circle. The measure of the angle is \(\theta .\) For each point \(P\) the \(x\) -coordinate and the quadrant is given. Find: a. the \(y\) -coordinate of \(P\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) \(\left(-\frac{\sqrt{2}}{2}, y\right),\) third quadrant

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 150^{\circ} $$

In \(3-44,\) find the exact value. $$ \sin 60^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(210^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \cos 25^{\circ} $$

In \(3-10,\) the terminal side of \(\angle R O P\) in standard position intersects the unit circle at \(P .\) If \(\mathrm{m} \angle R O P\) is \(\theta,\) find: a. \(\sin \theta\) b. \(\cos \theta\) c.tan \(\theta\) d. \(\sec \theta\) e. \(\csc \theta\) f. \(\cot \theta\) $$ P\left(-\frac{2 \sqrt{10}}{7},-\frac{3}{7}\right) $$

In \(3-11, P\) is the point at which the terminal side of an angle in standard position intersects the unit circle. The measure of the angle is \(\theta .\) For each point \(P\) the \(x\) -coordinate and the quadrant is given. Find: a. the \(y\) -coordinate of \(P\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) \(\left(\frac{1}{5}, y\right),\) fourth quadrant

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 200^{\circ} $$

The lengths of the sides of \(\triangle A B C\) are given. For each triangle, \(\angle C\) is the right angle and \(\mathrm{m} \angle A<\mathrm{m} \angle B .\) Find: a. \(\sin A\) b. \(\cos A\) c. \(\tan A\). \(6,3 \sqrt{5}, 9\)

In \(3-44,\) find the exact value. $$ \csc 60^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(250^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \cos 75^{\circ} $$

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. \(\cot \theta\) \((3,4)\)

In \(11-14,\) for each of the following function values, find \(\theta\) if \(0^{\circ} \leq \theta < 360^{\circ}\) $$ \begin{array}{l}{\sin \theta=1} \\ {\cos \theta=0}\end{array} $$

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ 300^{\circ} $$

Use an isosceles right triangle with legs of length 3 to find the exact values of \(\sin 45^{\circ},\) \(\cos 45^{\circ},\) and \(\tan 45^{\circ} .\)

In \(3-44,\) find the exact value. $$ \tan 60^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(285^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 280^{\circ} $$

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. \(\cot \theta\) \((1,4)\)

In \(3-11, P\) is the point at which the terminal side of an angle in standard position intersects the unit circle. The measure of the angle is \(\theta .\) For each point \(P\) the \(x\) -coordinate and the quadrant is given. Find: a. the \(y\) -coordinate of \(P\) b. \(\cos \theta\) c. \(\sin \theta\) d. \(\tan \theta\) \(\left(-\frac{\sqrt{7}}{3}, y\right),\) second quadrant

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ -75^{\circ} $$

Use an equilateral triangle with sides of length 4 to find the exact values of \(\sin 30^{\circ}, \cos 30^{\circ},\) and \(\tan 30^{\circ} .\)

In \(3-44,\) find the exact value. $$ \cot 60^{\circ} $$

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(310^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 80^{\circ} $$

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. \(\cot \theta\) \((-3,-3)\)

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ -200^{\circ} $$

A 20-foot ladder leaning against a vertical wall reaches to a height of 16 feet. Find the sine, cosine, and tangent values of the angle that the ladder makes with the ground.

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

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(95^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 375^{\circ} $$

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. \(\cot \theta\) \((-5,-5)\)

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. \(\tan \theta\) $$ (8,15) $$

In \(11-14,\) for each of the following function values, find \(\theta\) if \(0^{\circ} \leq \theta < 360^{\circ}\) $$ \begin{array}{l}{\sin \theta=0} \\ {\cos \theta=-1}\end{array} $$

In \(8-17,\) name the quadrant in which an angle of each given measure lies. $$ -280^{\circ} $$

An access ramp reaches a doorway that is 2.5 feet above the ground. If the ramp is 10 feet long, what is the sine of the angle that the ramp makes with the ground?

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

In \(8-17,\) for each angle with the given degree measure, find the measure of the reference angle. \(290^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 15^{\circ} $$

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. \(\cot \theta\) \((-6,6)\)

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. \(\tan \theta\) $$ (-1,-1) $$