Question

How do you find the values of `theta` given `sectheta=sqrt2`?

Answer 1

General solution : `theta = (2 n pi + pi/4) , theta = (2 n pi + (7pi)/4)` , where n is an integer `[n = 0, 1, 2,3 ,.........]`

Explanation:

`sec theta = sqrt 2 :. cos theta = 1/sqrt 2 ; cos 45^0 = 1/sqrt 2 , cos (360-45) =cos 315= 1/sqrt 2 :. theta = 45^0 (pi/4), 315^0((7pi)/4)` Note: `cos theta` is positive in 1st and last quadrant.

General solution : `theta = (2 n pi + pi/4) , theta = (2 n pi + (7pi)/4)` where n is an integer `[n = 0, 1, 2,3 ,.........]` [Ans]