Books(current) Courses (current) Earn 💰 Log in(current)

Algebra 2 and Trigonometry

Ann Xavier Gantert

Chapter 12

TRIGONOMETRIC IDENTITIES

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?

Check back soon!

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.
Numerade Educator

Problem 3

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

Check back soon!

Problem 4

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

Yoshihito T.
Numerade Educator

Problem 5

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

Check back soon!

Problem 6

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

Yoshihito T.
Numerade Educator

Problem 7

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

Check back soon!

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.
Numerade Educator

Problem 9

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

Check back soon!

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.
Numerade Educator

Problem 11

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

Check back soon!

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.
Numerade Educator

Problem 13

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

Check back soon!

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.
Numerade Educator