Chapter 7: Q. 2 (page 505)

Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (- \frac{\sqrt{2}}{2})$

Short Answer

Expert verified

The exact value of the given expression is $- \frac{π}{4}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\sin^{- 1} (- \frac{\sqrt{2}}{2})$

Assume $θ = \sin^{- 1} (- \frac{\sqrt{2}}{2})$

As $y = \sin^{- 1} x$ means $x = \sin y$ , where,

$- \frac{π}{2} \leq θ \leq \frac{π}{2}$

Rewrite the function,

$\sin θ = - \frac{\sqrt{2}}{2}$

Step 2. Determine the interval.

The only angle $θ$ within the interval $[- \frac{π}{2}, \frac{π}{2}]$ whose sine is $- \frac{\sqrt{2}}{2}$ is given below,

$- \frac{π}{4}$

Then, we can say,

localid="1646501876925" $\sin θ = - \frac{\sqrt{2}}{2} \sin θ = \sin (- \frac{π}{4}) θ = - \frac{π}{4}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (- \frac{\sqrt{2}}{2})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the interval.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the exact value of the expression. Express angles in radians.sin-1-22

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the interval.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (- \frac{\sqrt{2}}{2})$