Given that tan x =, find cos (90 - x)º giving the answer to 4 significant figures

Answer 1

You didn't state the value of tanx
suppose tanx = 4/5
using the standard x,y, and r definitions
tanØ = y/x
then r^2 = x^2 + y^2 = 16 + 25 = 41
then r = √41

but sinx = cos(90-x)°, (property of complementary angles)
so cos(90-x) = sinx = 4/√41
use your calculator to find that value correct to 4 significants

So whatever your given value is for tanx
simply follow the same steps

Answer 2

as Reiny noted, sinx = cos(90-x)
so, if you have tanx = y, then
cos(90-x) = sinx = 1/cscx = 1/√(1+cot^2x) = 1/√(1 + 1/y^2)