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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?

 Jan 8, 2019
 #1
avatar+18346 
+2

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  

 Jan 8, 2019
edited by ElectricPavlov  Jan 8, 2019
 #2
avatar+100546 
+1

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

 

 

cool cool cool

 Jan 8, 2019

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