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. $$ -45^{\circ} $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ -85^{\circ} $$

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

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\sin 285^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 88^{\circ} 30^{\prime} $$

What is the smallest positive value of \(\theta\) such that \(\cos \theta=0 ?\)

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. $$ \sin \theta<0, \cos \theta<0 $$

If \(P\left(\frac{2}{3}, y\right)\) is a point on the unit circle and on the terminal side of an angle in standard position with measure \(\theta,\) find: a. \(y\) b. \(\sin \theta\) c. \(\cos \theta\)

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ -270^{\circ} $$

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

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\cos 245^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 105^{\circ} 50^{\prime} $$

Grace walked within range of a cell phone tower. As soon as her cell phone received a signal, she looked up at the tower. The cotangent of the angle of elevation of the top of the tower is \(\frac{1}{10} .\) If the top of the tower is 75 feet above the ground, to the nearest foot, how far is she from the cell phone tower?

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. $$ \sin \theta>0, \tan \theta>0 $$

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ -500^{\circ} $$

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

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\tan 305^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 172^{\circ} 18^{\prime} $$

A pole perpendicular to the ground is braced by a wire 13 feet long that is fastened to the ground 5 feet from the base of the pole. The measure of the angle the wire makes with the ground is \(\theta .\) Find the value of: $$\begin{array}{llll}{\text { a. } \sec \theta} & {\text { b. } \csc \theta} & {\text { c. } \cot \theta}\end{array}$$

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. $$ \tan \theta<0, \cos \theta<0 $$

Under a reflection in the \(y\) -axis, the image of \(A(x, y)\) is \(A^{\prime}(-x, y)\) . The measure of \(\angle R O P=\theta\) and \(P(\cos \theta, \sin \theta)\) is a point on the terminal side of \(\angle R O P .\) Let \(P^{\prime}\) be the image of \(P\) and \(R^{\prime}\) be the image of \(R\) under a reflection in the \(y\) -axis. a. What are the coordinates of \(P^{\prime} ?\) b. Express the measure of \(\angle R^{\prime} O P^{\prime}\) in terms of \(\theta\) c. Express the measure of \(\angle R O P^{\prime}\) in terms of \(\theta\)

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ 540^{\circ} $$

In \(3-44,\) find the exact value. $$ \cos 270^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\sin -56^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \cos 205^{\circ} 12^{\prime} $$

An airplane travels at an altitude of 6 miles. At a point on the ground, the measure of the angle of elevation to the airplane is \(\theta .\) Find the distance to the plane from the point on the ground when: $$ \csc \theta=2 \quad \text { b. } \sec \theta=\frac{5}{3} \quad \text { c. } \cot =\sqrt{3} $$

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. $$ \sin \theta<0, \tan \theta>0 $$

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

In \(3-44,\) find the exact value. $$ \sec 270^{\circ} $$

In \(18-27\) , express each given function value in terms of a function value of a positive acute angle (the reference angle). \(\sin 500^{\circ}\)

In \(3-38,\) find each function value to four decimal places. $$ \sin 205^{\circ} 12^{\prime} $$

When \(\sin \theta=-1,\) find a value of: \(\quad\) a. \(\cos \theta \quad\) b. \(\tan \theta \quad\) c. \(\theta\)

In \(18-27,\) for each given angle, find a coterminal angle with a measure of \(\theta\) such that \(0 \leq \theta < 360\). $$ 980^{\circ} $$

In \(3-44,\) find the exact value. $$ \sin 270^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=0.3420\)

In \(3-38,\) find each function value to four decimal places. $$ \tan 266^{\circ} 27^{\prime} $$

Show that \(\cot \theta=\frac{\cos \theta}{\sin \theta}\) for all values of \(\theta\) for which \(\sin \theta \neq 0\)

When \(\tan \theta=0,\) find a value of: \(\quad\) a. \(\sin \theta \quad\) b. \(\cos \theta \quad \mathbf{c} . \theta\)

Do the wheels of a car move in the clockwise or counterclockwise direction when the car is moving to the right of a person standing at the side of the car?

In \(3-44,\) find the exact value. $$ \csc 270^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\cos \theta=0.6283\)

In \(3-38,\) find each function value to four decimal places. $$ \sec 72^{\circ} $$

When tan \(\theta\) is undefined, find a value of: \(\quad\) a. \(\sin \theta \quad \mathbf{b} \cdot \cos \theta \quad \mathbf{c} . \theta\)

To remove the lid of a jar, should the lid be turned clockwise or counterclockwise?

In \(3-44,\) find the exact value. $$ \tan 270^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\tan \theta=0.3240\)

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

Angle \(R O P\) is an angle in standard position with \(\mathrm{m} \angle R O P=\theta, R(1,0)\) a point on the initial side of \(\angle R O P\) and \(P(p, q)\) the point at which the terminal side of \(\angle R O P\) intersects the unit circle. a. What is the domain of \(\cos \theta\) and of \(\sin \theta ?\) b. What is the range of \(\cos \theta\) and of \(\sin \theta\) ? c. Is tan \(\theta\) defined for all angle measures? d. What is the domain of \(\tan \theta ?\) e. What is the range of \(\tan \theta ?\)

a. To insert a screw, should the screw be turned clockwise or counterclockwise? b. The thread spirals six and half times around a certain screw. How many degrees should the screw be turned to insert it completely?

In \(3-44,\) find the exact value. $$ \cot 270^{\circ} $$