Chapter 6: Q. 12 (page 419)

For what numbers $x, - 2 π \leq x \leq 2 π$ does $c s c x = 1 ?$ For what numbers x does $c s c x = - 1 ?$

Short Answer

Expert verified

For $x = \frac{π}{2}, - \frac{3 π}{2}, c s c x = 1$ and for $x = - \frac{π}{2}, \frac{3 π}{2}, c s c x = - 1 .$

Step by step solution

Step 1. Given Information

We have to find for what numbers do $c s c x = 1 a n d c s c x = - 1 .$

Step 2. Finding the numbers

As we know the reciprocal of the cosecant function is $\frac{1}{\sin} .$

So, $c s c x = 1 w h e n \sin x = 1 .$

The sine functions are $1$ at $\frac{π}{2} a n d - \frac{3 π}{2}$ in the given interval.

Thus, $c s c x = 1$ will be at $\frac{π}{2} a n d - \frac{3 π}{2} .$

Step 3. Finding the numbers

Likewise, the cosecant function is $- 1$ , when sine function is $- 1 .$

The sine function is $- 1$ at role="math" localid="1646400679548" $- \frac{π}{2} a n d \frac{3 π}{2}$ in the given interval.

Thus, the cosecant function is $- 1$ at role="math" localid="1646400699176" $- \frac{π}{2} a n d \frac{3 π}{2}$ in the given interval.

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For what numbers $x, - 2 π \leq x \leq 2 π$ does $c s c x = 1 ?$ For what numbers x does $c s c x = - 1 ?$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the numbers

Step 3. Finding the numbers

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For what numbers x,-2π≤x≤2πdoes cscx=1? For what numbers x doescscx=-1?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the numbers

Step 3. Finding the numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Logic and Functions

Applied Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

For what numbers $x, - 2 π \leq x \leq 2 π$ does $c s c x = 1 ?$ For what numbers x does $c s c x = - 1 ?$