determining an exact measure of all the angles that satisfy the following?

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598

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I need to find sec θ = \({2}\) in the domain \({-180° ≤ θ < 90°}\)

because sec θ = \({1 \over cosθ}\), and cos 60° = 2 (using the half equilateral triangle), i know my angles are 60°, -60°, -120°, and -180°.

but in the textbook, the answers are 60°and -60°. i'm confused? my answers fit in the domain so why aren't they considered as an answer?

Guest Jan 8, 2019

ElectricPavlov · Answer 1 · 2019-01-08T09:35:16

Sec = 1/cos

1/cos =2

1 = 2 cos

1/2 = cos 60 degrees and -60 degrees Cos of -120 = -1/2 cos of -180 = -1

CPhill · Answer 2 · 2019-01-08T09:39:19

The secant will only be positive where the cosine is positive

From - 180 to -90 the cosine is negative

From (-90 to 90 ) the cosine is positive

Note sec θ = 2 means that cos θ = 1/2

And this happens at -60° and 60° on the requested interval