# Algebra 2 and Trigonometry

## Educators

Problem 1

If we know the value of $\sin \theta,$ is it possible to find the other five trigonometric function values? If not, what other information is needed?

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Problem 2

a. Explain how the identities $1+\tan ^{2} \theta=\sec ^{2} \theta$ and $\cot ^{2} \theta+1=\csc ^{2} \theta$ can be derived from the identity $\cos ^{2} \theta+\sin ^{2} \theta=1$
b. The identity $\cos ^{2} \theta+\sin ^{2} \theta=1$ is true for all real numbers. Are the identities $1+\tan ^{2} \theta=\sec ^{2} \theta$ and $\cot ^{2} \theta+1=\csc ^{2} \theta$ also true for all real numbers? Explain your answer.

Yoshihito T.

Problem 3

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\tan \theta$$

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Problem 4

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\cot \theta$$

Yoshihito T.

Problem 5

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\sec \theta$$

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Problem 6

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\csc \theta$$

Yoshihito T.

Problem 7

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\cot \theta \sec \theta$$

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Problem 8

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\tan ^{2} \theta+1$$

Yoshihito T.

Problem 9

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\cot ^{2} \theta+1$$

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Problem 10

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\tan \theta \sec \theta \cot \theta$$

Yoshihito T.

Problem 11

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\frac{1}{\sec \theta \csc \theta}$$

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Problem 12

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\frac{\tan \theta}{\cot \theta}+\tan \theta \cot \theta$$

Yoshihito T.

Problem 13

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\frac{1}{\tan \theta}+\cot \theta$$

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Problem 14

In $3-14,$ write each expression as a single term using $\sin \theta, \cos \theta,$ or both.
$$\sec \theta+\frac{1}{\csc \theta}$$

Yoshihito T.