given tan theta=-2 and pi/2 less than theta less than pi; find cos2 theta

Answer 1

if tanθ=-2 and θ between 90 and 180 degrees

then cosθ=-1/√5 and sinθ=2/√5

know cos2θ=cos²θ-sin²θ

here cos2θ=(1/5)-4/5=-3/5

Answer 2

Tan = y/x.

-2 = -2 / 1

(-1)*(-1) + 2*2 = 5

Note: theta must be in the second quadrant because theta is between π/2 and π. y is positive here and x is negative here.

Hypotenuse (in ratio) = √5

Cos² (1/√5) = ?

Use the cosine inverse on your calculator.