Chapter 5.5, Problem 45E

(a)

To determine

To explain: if ${\sin }^{-1}2.4567$ is impossible or not

Explanation of Solution

Given information: Critical Thinking

Calculation:

Sine (and cosine) are cyclic functions whose ratio never exceed 1 or − 1,

So it is impossible to find and angle that is going to give you a sine value of 2.4567.

(b)

To determine

To explain: if ${\sec }^{-1}0.5239$ is impossible or not.

Explanation of Solution

Given information: Critical Thinking

Calculation:

Since secant is 1 / cosine and cosine cannot exceed 1,

The denominator of secant is always between 0 and 1.

The numerator of secant is 1. If you divide a number by a number between 0 and 1, the number always gets bigger,

So the numerator of secant can never be less than 1.

(c)

To determine

To explain: if ${\cos }^{-1}\left(-3.4728\right)$ is impossible or not.

Explanation of Solution

Given information: Critical Thinking

Calculation:

Cosine (and sine) are cyclic functions whose ratio never exceed 1 or − 1,

So it is impossible to find and angle that is going to give you a cosine value of − 3.4728.