Let costheta 1squareroot 10 with theta Quadrant III Without

Let cos(theta) = -1/squareroot 10 with theta Quadrant III. Without using a calculator find the following: sin(2 theta) = cos(2 theta) = cos^2 theta - sin^2 theta = 1-2 sin^2 theta = 2 cos^2 theta - 1

Solution

cos = -1/10

sin = (1 - 1/10) = -3/10

a) sin2 = 2*sin*cos = 2*(-3/10)*(-1/10) = 6/10 = 3/5

b) cos2 = 2*cos^2 - 1 = 2/10 - 1 = -8/10 = -4/5