Given that tan x =3k and x is an acute angle,find the value of each of the following trigonometric function in terms of k.

Question

a)cot x

b)cosec x

c)sec x

Answer 1

acute angle is 1st quadrant where all trig functions are positive.

Tangent has range between zer0 and infinity, and most importantly positive.

So the triangle is in quadrant #1, with x=1 (the agjacent) and y = 3k (the opposite).

The hypotenuse by pythagorean theorem is sqrt(9k^2+1)

the trig functions are:

sine = 3k/(sqrt(9k^2+1))

ciosine = 1/sqrt(9k^2+1)

tangent = 3k

cosecant = sqrt(9k^2+1)/(3k)

cosecant = sqrt(9k^2+1)

cotangent = 1/(3k)