Question

If `x` represents the radian measure of an angle, where `0<=x<=pi/2` and `sinx=5/13`, then what is the value of `tan(pi/2-x)`?

Answer 1

`12/5`

Explanation:

`sin x = 5/13`.
First, find cos x by the identity: `cos^2 x = 1 - sin^2 x`
`cos^2 x = 1 - 25/169 = 144/169` --> `cos x = +- 12/13`.
Since x is in Quadrant I, cos x is positive.
`tan x = sin/(cos) = (5/13)(13/12) = 5/12`
Property of complementary arcs:
`tan (pi/2 - x) = cot x = 1/(tan x)`
There for:
`tan (pi/2 - x) = 12/5`