tough question

Question

GIVEN THAT SINθ= -11/61 AND θ IN QUADRANT IV DETERMINES SIN 2θ, COS 2θ, TAN 2θ. WHICH QUADRANT IS 2θ IN.

 

 

SIN 2θ=     COS 2θ=    TAN 2θ= 

Answer 1

Using the Pythagorean Theorem, we can see that this is an 11-60-61 right triangle. Therefore we can used this to find the trigonometric functions for θ.

 

sin θ = -11/61

cos θ = 60/61

 

sin 2θ = 2*sin θ * cos θ = 2(-11/61)(60/61) = -1320/3721

 

cos 2θ = (cos θ)^2 - (sin θ)^2 = (60/61)^2 - (-11/61)^2 = 3600/3721 - 121/3721 = 3479/3721

 

tan 2θ = (sin 2θ)/(cos 2θ) = -1320/3479