If tan(x) = −9 and x is in quadrant IV, find the exact values of the expressions without solving for x. a.) sin(2x) b.) cos(2x) c.) tan(2x)

Answer 1

x=arctan(-9) = -83.609858.....

tan = opp/adj = -9/1 <-- quadrant 4

x=1 and y=-9 ---> (1,-9)

hypotenuse is sqrt( 1 + 81) = sqrt(82)

the answers are

.

Answer 2

Using SOHCAHTOA, tanx = -9, sinx = -9/√82, and cosx = 1/√82.

So, sin(2x) = 2(sinx)(cosx) = -18/82 = -9/41, cos(2x) = cos²x - sin²x = -80/82 = -40/41, and

tan(2x) = sin(2x) / cos(2x) = 9/40