Question

The acute angle x radians is such that tan x = k, where k is a positive constant. Express, in terms of k,
(i) tan(pi − x),
(ii) tan(pi/2 − x),
(iii) sin x.

Answer 1

tangent is periodic with period \(\pi\) and so \(\tan(\pi-x)=\tan(-x)\) but since tangent is odd, \(\tan(-x)=-\tan(x)\)

Answer 2

?

Answer 3

1. -tan(x) i.e -k
2.cot(x ) i.e. 1/k
3.k/(sqrt(1+(k^2)))