Find the exact value of each expression. (a) tan(sec^-1 4) (b) sin(2 sin^-1((3)/(5)))

Name: Problem 6, Chapter 3: Essential Calculus Early Transcendentals
Uploaded: 2020-06-10T00:00:34-08:00
Duration: 1 min 50 s
Channel: Ernest Castorena
Description: Find the exact value of each expression. (a) tan(sec^-1 4) (b) sin(2 sin^-1((3)/(5)))

step 1 value of each expression. So remember, this is just secant is just one over cosine. So let's see

Question

Find the exact value of each expression. (a) $\tan \left(\sec ^{-1} 4\right)$ (b) $\sin \left(2 \sin ^{-1}\left(\frac{3}{5}\right)\right)$

   Find the exact value of each expression.
(a) $\tan \left(\sec ^{-1} 4\right)$ (b) $\sin \left(2 \sin ^{-1}\left(\frac{3}{5}\right)\right)$

Essential Calculus Early Transcendentals

James Stewart 2nd Edition

Chapter 3, Problem 6

Instant Answer

Solved by Expert Ernest Castorena

06/10/2020

Step 1

We know that secant is the reciprocal of cosine, so $\sec ^{-1} 4$ is the angle whose secant is 4. In a right triangle, secant is the ratio of the hypotenuse to the adjacent side. So, if we consider a right triangle with hypotenuse 4 and adjacent side 1, we can Show more…

Show all steps

Thanks for your feedback!

Find the exact value of each expression. (a) $\tan \left(\sec ^{-1} 4\right)$ (b) $\sin \left(2 \sin ^{-1}\left(\frac{3}{5}\right)\right)$

Play audio

Feedback

Ernest Castorena and 92 other subject Calculus 1 / AB 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

Inverse Trigonometric Functions

These functions are used to retrieve the angle whose trigonometric function has a given value. They ensure that every trigonometric value corresponds to a unique angle within a specific interval, which is crucial when converting back and forth between angles and ratios.

Pythagorean Identity

This fundamental identity, such as sin²? + cos²? = 1 and its derived forms (e.g., sec²? - tan²? = 1), is essential for relating different trigonometric functions. It plays a key role when one function's value is known and another function’s value needs to be determined in an expression.

Double Angle Formula

The double angle formula, for instance sin(2?) = 2 sin? cos?, allows one to express trigonometric functions of double angles in terms of the functions of the original angle. This is particularly useful when an expression involves the sine or cosine of a doubled angle, and the corresponding single-angle values are known.

Please give Ace some feedback