Question

Given $\sec \theta = 11$, use trigonometric identities to find the exact value of the following expressions. (a) $\cos \theta$ (b) $\tan^2 \theta$ (c) $\csc (90^\circ - \theta)$ (d) $\csc^2 \theta$

          Given $\sec \theta = 11$, use trigonometric identities to find the exact value of the following expressions.
(a) $\cos \theta$
(b) $\tan^2 \theta$
(c) $\csc (90^\circ - \theta)$
(d) $\csc^2 \theta$
        
Given secθ = 11, use trigonometric identities to find the exact value of the following expressions.
(a) cosθ
(b) tan^2 θ
(c) csc (90^∘ - θ)
(d) csc^2 θ

Added by Edward G.

Close

Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Given sec heta =11, use trigonometric identities to find the exact value of the following expressions. (a) cos heta (b) tan^(2) heta (c) csc(90deg - heta ) (d) csc^(2) heta Given sec =11,use trigonometric identities to find the exact value of the following expressions K< (a)cose (b) tan2e (c)csc(90-0) (d) csc2e
Close icon
Play audio
Feedback
Powered by NumerAI
Jennifer Stoner Ivan Kochetkov
David Collins verified

Christopher Stanley and 89 other subject Precalculus educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
applying-trigonometric-ldentities-use-the-given-function-values-and-the-trigonometric-identities-t-3

Applying Trigonometric ldentities, use the given function value(s) and the trigonometric identities to find the indicated trigonometric functions. $$\cos \theta=\frac{1}{3}$$ $$\begin{array}{ll}{\text { (a) } \sin \theta} & {\text { (b) } \tan \theta} \\ {\text { (c) } \sec \theta} & {\text { (d) } \csc \left(90^{\circ}-\theta\right)}\end{array}$$

Precalculus with Limits

Trigonometry

Right Triangle Trigonometry

use-the-given-function-values-and-the-trigonometric-identities-to-find-the-exact-value-of-each-ind-3

Use the given function value(s) and the trigonometric identities to find the exact value of each indicated trigonometric function. $\cos \theta=\frac{1}{3}$ (a) $\sin \theta$ (b) $\tan \theta$ (c) sec $\theta$ (d) $\csc \left(90^{\circ}-\theta\right)$

Precalculus

Trigonometry

Right Triangle Trigonometry

use-the-given-function-values-and-trigonometric-identities-including-the-cofunction-identities-to--8

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. $\cos \theta=\frac{1}{3}$ (a) $\sin \theta$ (b) $\tan \theta$ (c) $\sec \theta$ (d) $\csc \left(90^{\circ}-\theta\right)$

Precalculus: A Concise Course

Trigonometry

Right Triangle Trigonometry


*

Recommended Textbooks

-
Precalculus with Limits

Precalculus with Limits

Ron Larson 2nd Edition
achievement 1,631 solutions
Precalculus

Precalculus

Robert Blitzer 5th Edition
achievement 1,372 solutions
Precalculus

Precalculus

Jay Abramson 1st Edition
achievement 1,081 solutions

*

Transcript

-
00:01 Here on this problem, we've been told that the cosine of theta is equal to one -third.
00:04 And when we want to use identities to find other trick functions here, starting with the sign of theta.
00:10 Now, the sign of theta is equal to the square root of one minus the cosine squared of theta.
00:17 So since the cosine is one -third, this tells us that this is equal to one minus one -third squared, which is equal to the square root of one minus one over nine, which is equal to the square root of eight over nine, which is 2 root 2 over 3.
00:44 And so the sine of theta is equal to 2 root 2 over 3.
00:52 Now in part b, we're looking for the tangent of theta.
00:59 Now the tangent of theta, as we know, is equal to the sine of theta over the cosine of theta.
01:07 The sine of theta is 1 3.
01:10 I'm sorry, the sine of theta is 2 root 2 over 3, and the cosine of theta is 1 3...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever