Chapter 10

In \(15-23,\) use a calculator to find each value of \(\theta\) to the nearest degree. $$ \theta=\arccos 0.9 $$

In \(15-22,\) write each given expression in terms of sine and cosine and express the result in simplest form. \(\sec \theta+\tan \theta\)

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. $$ \tan \theta=1.5277 $$

In \(13-22\) , find the degree measure of each angle whose radian measure is given. 3\(\pi\)

In \(3-22 :\) a. Rewrite each function value in terms of its cofunction. b. Find, to four decimal places, the value of the function value found in a. $$ \sin 295^{\circ} $$

In \(15-23,\) use a calculator to find each value of \(\theta\) to the nearest degree. $$ \theta=\arccos (-0.9) $$

In \(15-22,\) write each given expression in terms of sine and cosine and express the result in simplest form. \(\frac{\sec \theta}{\csc \theta}\)

List five values of \(\theta\) for which cot \(\theta\) is undefined.

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. $$ \cot \theta=1.5277 $$

In \(13-22\) , find the degree measure of each angle whose radian measure is given. \(\frac{11 \pi}{6}\)

In \(3-22 :\) a. Rewrite each function value in terms of its cofunction. b. Find, to four decimal places, the value of the function value found in a. $$ \cot 312^{\circ} $$

In \(15-23,\) use a calculator to find each value of \(\theta\) to the nearest degree. $$ \theta=\arcsin 0.72 $$

In \(15-22,\) write each given expression in terms of sine and cosine and express the result in simplest form. \(\csc ^{2} \theta-\frac{\cot \theta}{\tan \theta}\)

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. $$ \sec \theta=5.232 $$

In \(13-22\) , find the degree measure of each angle whose radian measure is given. \(\frac{7 \pi}{2}\)

In \(15-23,\) use a calculator to find each value of \(\theta\) to the nearest degree. $$ \theta=\arcsin (-0.72) $$

In \(15-22,\) write each given expression in terms of sine and cosine and express the result in simplest form. \(\sec \theta(1+\cot \theta)-\csc \theta(1+\tan \theta)\)

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. $$ \cot \theta=0.3276 $$

If \(\sin \theta=\cos (20+\theta),\) what is the value of \(\theta ?\)

In \(15-23,\) use a calculator to find each value of \(\theta\) to the nearest degree. $$ \theta=\arctan (-17.3) $$

In \(23-27,\) for each angle with the given radian measure: a. Give the measure of the angle in degrees. b. Give the measure of the reference angle in radians c. Draw the angle in standard position and its] reference angle as an acute angle formed by the terminal side of the angle and the \(x\) -axis. \(\frac{\pi}{3}\)

For what value of \(x\) does \(\tan (x+10)=\cot (40+x) ?\)

In \(24-32,\) find the exact value of each expression. $$ \sin (\arctan 1) $$

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. $$ \cot \theta=0.1983 $$

In \(23-27,\) for each angle with the given radian measure: a. Give the measure of the angle in degrees. b. Give the measure of the reference angle in radians c. Draw the angle in standard position and its] reference angle as an acute angle formed by the terminal side of the angle and the \(x\) -axis. \(\frac{7 \pi}{36}\)

Complete the following table of cofunctions for radian values. $$ \begin{array}{|c|c|}\hline \text { Cofunctions (degrees) } & {\text { Cofunctions (radians) }} \\ \hline \cos \theta=\sin \left(90^{\circ}-\theta\right) & {\sin \theta=\cos \left(90^{\circ}-\theta\right)} & {} \\ \hline \tan \theta=\cot \left(90^{\circ}-\theta\right) & {\cot \theta=\tan \left(90^{\circ}-\theta\right)} & {} \\ \hline \sec \theta=\csc \left(90^{\circ}-\theta\right) & {\csc \theta=\sec \left(90^{\circ}-\theta\right)} & {} \\ \hline\end{array} $$

In \(24-32,\) find the exact value of each expression. $$ \cos (\arctan 0) $$

If \(\mathrm{f}(x)=\sin \left(\frac{1}{3} x\right),\) find \(\mathrm{f}\left(\frac{\pi}{2}\right)\)

In \(23-27,\) for each angle with the given radian measure: a. Give the measure of the angle in degrees. b. Give the measure of the reference angle in radians c. Draw the angle in standard position and its] reference angle as an acute angle formed by the terminal side of the angle and the \(x\) -axis. \(\frac{10 \pi}{9}\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \sin \frac{\pi}{3} $$

In \(24-32,\) find the exact value of each expression. $$ \tan (\arccos 1) $$

If \(\mathrm{f}(x)=\cos 2 x,\) find \(\mathrm{f}\left(\frac{3 \pi}{4}\right)\)

In \(23-27,\) for each angle with the given radian measure: a. Give the measure of the angle in degrees. b. Give the measure of the reference angle in radians c. Draw the angle in standard position and its] reference angle as an acute angle formed by the terminal side of the angle and the \(x\) -axis. \(-\frac{7 \pi}{18}\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \cos \frac{\pi}{4} $$

In \(24-32,\) find the exact value of each expression. $$ \cos (\arccos (-1)) $$

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. If \(\mathrm{f}(x)=\sin 2 x+\cos 3 x,\) find \(\mathrm{f}\left(\frac{\pi}{4}\right)\)

In \(23-27,\) for each angle with the given radian measure: a. Give the measure of the angle in degrees. b. Give the measure of the reference angle in radians c. Draw the angle in standard position and its] reference angle as an acute angle formed by the terminal side of the angle and the \(x\) -axis. \(\frac{25 \pi}{9}\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \tan \frac{\pi}{6} $$

In \(24-32,\) find the exact value of each expression. $$ \tan \left(\arcsin \left(-\frac{1}{2}\right)\right) $$

In \(13-24,\) find, to the nearest ten-thousandth, the radian measure \(\theta\) of a first-quadrant angle with the given function value. If \(\mathrm{f}(x)=\tan 5 x-\sin 2 x,\) find \(\mathrm{f}\left(\frac{\pi}{6}\right)\)

In \(28-37, \theta\) is the radian measure of a central angle that intercepts an arc of length \(s\) in a circle with a radius of length \(r .\) If \(s=6\) and \(r=1,\) find \(\theta\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \sec \frac{2 \pi}{3} $$

In \(24-32,\) find the exact value of each expression. $$ \cos \left(\arcsin \left(-\frac{\sqrt{3}}{2}\right)\right) $$

In \(28-37, \theta\) is the radian measure of a central angle that intercepts an arc of length \(s\) in a circle with a radius of length \(r .\) If \(\theta=4.5\) and \(s=9,\) find \(r\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \csc \frac{5 \pi}{6} $$

In \(24-32,\) find the exact value of each expression. $$ \tan \left(\arccos \left(-\frac{\sqrt{2}}{2}\right)\right) $$

In \(28-37, \theta\) is the radian measure of a central angle that intercepts an arc of length \(s\) in a circle with a radius of length \(r .\) If \(\theta=2.5\) and \(r=10,\) find \(s\)

In \(26-33 :\) a. Rewrite each function value in terms of its cofunction. b. Find the exact value of the function value found in a. $$ \cot \pi $$

In \(24-32,\) find the exact value of each expression. $$ \sin \left(\arccos \left(-\frac{\sqrt{2}}{2}\right)\right) $$

The wheels of a cart that have a radius of 12 centimeters move in a counterclockwise direction for 20 meters. a. What is the radian measure of the angle through which each wheel has turned? b. What is sine of the angle through which the wheels have turned?