Question

If the tan(x)=3/2 in quadrant III, what is the trigonometric value of the sec(x)?

Answer 1

`- sqrt13/2`

Explanation:

Use the trig identity:
`1 + tan^2 x = sec^2 x`
`sec^2 x = 1 + 9/4 = 13/4`
`sec x = +- sqrt13/2`
Since x is in quadrant III, then cos x is negative. Therefor:
`sec x = - sqrt13/2`