find sin2x, cos2x, tan2x when tan(x)= -1/2

Question

sin2x =

 

cos2x =

 

tan2x =

Answer 1

You're dealing with Quadrant IV because tangent is negative and cosine is positive.  The reference triangle has -1 as the vertical leg, and 2 as the horizontal leg; hypotenuse is √5.

 

Therefore sin x = -1/√5 and cos x = 2/√5.  You can then plug these values, as needed, into the formula for double angles.

 

You can do this work yourself because the formulas should be well known to you, at this point in a Trigonometry class.