Find each of the following under the given conditions Enter

Find each of the following under the given conditions. (Enter the exact answer as a fraction. Decimal answers will not be accepted. Your answer should not contain sin, cos, or tan.)

sin(2x) =

tan(2x) =

Solution

tanx = -4/3 and (pi/2 <x <pi)

x is in IInd quadrant

cosx = - 3/5 ; sinx = 4/5    as sin is +ve in IInd quadrat and cos is -ve in IInd quad

sin2x = 2sinxcosx = 2(4/5)(-3/5) = -24/25

cos2x = 2cos^2x -1 = 2(-3/5)^2 -1 = -7/25