Question

If sec x = -3, and x lies in quadrant II, find tan
x/2

Answer 1

√2.

Explanation:

sec ^2x = 1 + tan^2 x

(-3)^2 = 1 + tan^2x

tan^2 x = 8

tan x = +/- 2√2

tan x/2 = tanx / sec x + 1

= -2√2 / -3 + 1

= -2√2 / -2

= √2

We take the negative tan because tan is negative in the second quadrant.