Tan and sin if sec=4sin>0

Question

Tan and sin if sec=4 Sin >0

Answer 1

Sec x = 4

Then cos x = 1/4

 

This implies the adjacent is 1 and the hypotenuse is 4

Use the pythagorean theorem to find the opposite:  

1^2 + b^2 = 4^2

1+b^2 = 16

b^2 = 15

b = sqrt 15

 

So since Sinx = opp/hyp

sin = sqrt15/4

 

And Tan = sin / cos

tan x = (sqrt15)/4 ÷ 1/4 = sqrt 15