Find the exact value of sin 2θ​, cos 2θ, and tan 2θ and the quadrant in which 2θ lies. Cos θ=-20/29, θ is in quadrant III?

Question

Thank you!

Answer 1

cosine is negative in quadrants 2 and 3

 

The MAIN ANGLE is angle theta T = inverse cosine (20/29) = 46.4

 

So the given angle is either 133.6 or 226.4

 

The values of the trig function at twice the angle are given in the following table

       

           133.6                    226.4
SIN     0.996614261      0.203889203
COS  -0.082219306      0.97899397
TAN   -12.12141424     0.208264003