Chapter 10

Mia said that if you know the sine value of each acute angle, then you can find any trigonometric function value of an angle of any measure. Do you agree with Mia? Explain why or why not.

Nicholas said that the restricted domain of the cosine function is the same as the restricted domain of the tangent function. Do you agree with Nicholas? Explain why or why not.

Nathan said that cot \(\theta\) is undefined for the values of \(\theta\) for which csc \(\theta\) is undefined. Do you agree with Nathan? Explain why or why not.

Alexia said that when \(\theta\) is a second-quadrant angle whose measure is in radians, the measure of the reference angle in radians is \(\pi-\theta .\) Do you agree with Alexia? Explain why or why not.

If \(\sin A=\frac{1}{2},\) is \(\cos A=\frac{\sqrt{3}}{2}\) always true? Explain why or why not.

Ethan said that the equations \(\cos ^{2} \theta=1-\sin ^{2} \theta\) and \(\sin ^{2} \theta=1-\cos ^{2} \theta\) are identities. Do you agree with Ethan? Explain why or why not.

Diego said that when \(\theta\) is the radian measure of an angle, the angle whose radian measure is \(2 \pi n+\theta\) is an angle with the same terminal side for all integral values of \(n .\) Do you agree with Diego? Explain why or why not.

If a wheel makes two complete revolutions, each spoke on the wheel turns through an angle of how many radians? Explain your answer.

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. $$ \sin 65^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arcsin \frac{1}{2} $$

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\sin \frac{\pi}{2}\)

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\sin \theta=\frac{1}{5}\) and \(\theta\) is in the second quadrant.

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \sin \frac{\pi}{4} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(30^{\circ}\)

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. $$ \cos 80^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arctan 1 $$

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\cos \frac{\pi}{2}\)

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\cos \theta=\frac{3}{4}\) and \(\theta\) is in the first quadrant.

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \tan \frac{\pi}{3} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(90^{\circ}\)

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. $$ \tan 54^{\circ} $$

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\tan \frac{\pi}{2}\)

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\cos \theta=-\frac{3}{4}\) and \(\theta\) is in the third quadrant.

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \cos \frac{\pi}{2} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(45^{\circ}\)

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. $$ \sin 86^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arctan (-1) $$

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\sec \frac{\pi}{2}\)

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\sin \theta=-\frac{2}{3}\) and \(\theta\) is in the fourth quadrant.

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \tan \frac{\pi}{6} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(120^{\circ}\)

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. $$ \csc 48^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arccos \left(-\frac{1}{2}\right) $$

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\sin \theta=\frac{2}{3}\) and \(\theta\) is in the second quadrant.

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\csc \frac{\pi}{2}\)

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \cos \frac{2 \pi}{3} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(160^{\circ}\)

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. $$ \sec 75^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arcsin \left(-\frac{1}{2}\right) $$

For each function value, write the value or tell why it is undefined. Do not use a calculator. \(\cot \frac{\pi}{2}\)

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \sin \frac{4 \pi}{3} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(135^{\circ}\)

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. $$ \cot 57^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arctan (-\sqrt{3}) $$

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\tan \theta=4\) and \(\theta\) is in the third quadrant.

In \(3-12\) , find the exact function value of each of the following if the measure of the angle is given in radians. $$ \tan \frac{5 \pi}{4} $$

In \(3-12,\) find the radian measure of each angle whose degree measure is given. \(225^{\circ}\)

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. $$ \cos 70^{\circ} $$

In \(3-14,\) find each value of \(\theta : \mathbf{a} .\) in degrees \(\mathbf{b} .\) in radians $$ \theta=\arcsin \left(-\frac{\sqrt{3}}{2}\right) $$

In \(3-14,\) for each given function value, find the remaining five trigonometric function values. \(\sec \theta=-8\) and \(\theta\) is in the second quadrant.