Evaluate the expression \cos\left(\sin^{-1}\left(\frac{8}{17}\right) + \tan^{-1}\left(\frac{8}{8}\right)\right). Give an exact answer.
Added by Donald B.
Close
Step 1
sin^(-1)((8)/(17)) is the angle whose sine is (8/17). Let's denote this angle as θ. Therefore, sin(θ) = 8/17. Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can find cos(θ) as follows: cos(θ) = sqrt(1 - sin^2(θ)) = sqrt(1 - (64/289)) = sqrt(225/289) = Show more…
Show all steps
Your feedback will help us improve your experience
Ramzi Deek and 82 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Value of an Expression Find the exact value of the expression. $$ \cos \left(\sin ^{-1} \frac{4}{5}\right) $$
Trigonometric Functions: Right Triangle
Inverse Trigonometric Functions and Right Triangles
Evaluate the given expression. $$\sin ^{-1}\left(\cos 40^{\circ}\right)$$
Transcendental Functions
The Inverse Trigonometric Functions
Evaluate each expression exactly. $$\cos \left[2 \sin ^{-1}\left(\frac{3}{5}\right)\right]$$
Analytic Trigonometry
Inverse Trigonometric Function
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD