find sin t and cos t from tan t

Question

if tan t= (2x-1)/x find sin t and cos t. assume both are positive.

Answer 1

tan t = sin t / cos t By definition, learn it

(2x - 1) / x = sin t / cos t

Can you answer now?

Answer 2

tangent is opposite/adjacent which are 2 of the 3 sides of the triangle. Can use Pythagorean theorem to calculate the third side which is the hypotenuse

(2x-1)^2 +x^2= h^2

4x^2 -4x+1 +x^2= h^2

5x^-4x+1=h^2

h= sqroot(5x^2-4x+1) so sine is (2x-1)^2/sqroot(5x^2 -4x +1) I will leave it to you to rationalize the denominator

cos= x^2/sqroot(5x^2-4x+1)