Chapter 7: Q. 5 (page 503)

In Problems 1– 8, find the exact value of each expression. Do not use a calculator.
$\cos^{- 1} (- \frac{\sqrt{3}}{2})$

Short Answer

Expert verified

The exact value is $\frac{5 π}{6}$ .

Step by step solution

Step 1. Definition

The inverse cosine function $y = \cos^{- 1} x$ means that $x = \cos y$ where $- 1 \leq x \leq 1$ and $0 \leq y \leq π$ .

Step 2. Find the exact value

Let $θ = \cos^{- 1} (- \frac{\sqrt{3}}{2})$ , so using the definition of inverse cosine function it can be written as $- \frac{\sqrt{3}}{2} = \cos θ$ where $0 \leq θ \leq π$ .

In this interval the angle for which the cosine value is $- \frac{\sqrt{3}}{2}$ is $\frac{5 π}{6}$ .

So the value of $\cos^{- 1} (- \frac{\sqrt{3}}{2})$ is $\frac{5 π}{6}$ .

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In Problems 1– 8, find the exact value of each expression. Do not use a calculator.
$\cos^{- 1} (- \frac{\sqrt{3}}{2})$

Short Answer

Step by step solution

Step 1. Definition

Step 2. Find the exact value

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In Problems 1– 8, find the exact value of each expression. Do not use a calculator.cos-1-32

Short Answer

Step by step solution

Step 1. Definition

Step 2. Find the exact value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Applied Mathematics

Discrete Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 1– 8, find the exact value of each expression. Do not use a calculator.
$\cos^{- 1} (- \frac{\sqrt{3}}{2})$