Question

9-34) if cos x = 0.45, then = each of the following could be the value of x, in radians, except

a) -1.10 - 2 pi

b) -1.10

c) 1.10

d) 1.10 + pi

e) 1.10 + 2 pi

how

Answer 1

d) 1.10 + pi

Explanation:

You want to know the angle listed whose cosine is not 0.45.

Cos(x) = 0.45

The value of x is found using the inverse cosine function:

x = arccos(0.45) ≈ 1.10

We know that cosine is an even function, so cos(-x) = cos(x). This means the angle can also be ...

x = -1.10

Since the cosine is periodic with period 2π, the values of x can be ...

x = ±1.10 +2nπ, where n is any integer

The value not on this list is ...

1.10 +π

The cosine of that angle is -0.45.

x is not 1.10 +π

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Additional comment

A calculator is useful for sorting this out.