Find two values of theta that satisfy the equation.

Question

Find two values of theta that satisfy the equation. Given your answer in degrees (0≤ theta≤360) and radians (0≤ theta≤2π)

a) sec theta=√2/2

Answer 1

sec is the reciprocal of cos

 

cos theta = 2/√2

However, cos theta can never be greater than 1.

There is no solution.

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Answer 2

sec Θ = √2/2

cos Θ = 2/√2

 

Θ = cos^-1 √2/2 = 45° or -45° or 360-45 = 315°

 

:)