Chapter 7: Q 40. (page 457)

In Problems 37-44, find the exact value of each expression.
$c s c^{- 1} (\sqrt{2})$

Short Answer

Expert verified

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

Step by step solution

Step 1. Write the given information.

The given expression is: $c s c^{- 1} (\sqrt{2})$ .

Use the trigonometric properties.

Using the property: $x = c s c^{- 1} (y) \Rightarrow c s c x = y$ .

So,

$θ = c s c^{- 1} (\sqrt{2}) \Rightarrow c s c θ = \sqrt{2}$ .

Use the trigonometric property.

Using the trigonometric property:

$\sin x = \frac{1}{c s c x} \Rightarrow c s c x = \frac{1}{\sin x}$ .

Thus,

$\sin (θ) = \frac{1}{c s c θ} \Rightarrow \sin (θ) = \frac{1}{\sqrt{2}} \Rightarrow θ = \frac{π}{4}$ .

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In Problems 37-44, find the exact value of each expression.
$c s c^{- 1} (\sqrt{2})$

Short Answer

Step by step solution

Step 1. Write the given information.

Use the trigonometric properties.

Use the trigonometric property.

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In Problems 37-44, find the exact value of each expression.csc-1(2)

Short Answer

Step by step solution

Step 1. Write the given information.

Use the trigonometric properties.

Use the trigonometric property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Geometry

Study anywhere. Anytime. Across all devices.

In Problems 37-44, find the exact value of each expression.
$c s c^{- 1} (\sqrt{2})$