Solve 2 sin x cos x sin x 0 in the interval Evaluate cos t

Solve 2 sin x cos x - sin x = 0 in the interval Evaluate cos (tan^-1) If tan = 3/4 and sin = 0, find cos B. A ship leaves P a bearing of 32 degree and travels 9 miles. Then the turns due and travels 6 miles. How far is the ship from port?

Solution

6)a) 2*sin x * cos x - sin x = 0

sinx(2*cos x - 1) = 0

sin x = 0 ======> x = 0, 180

cos x = 1/2 ========> x = 60, 300

b) cos(tan^-1 1) = cos45 = 0.707

7)  9cos32 + 6 = x component
9sin32 + 0 = y component

Total distance of ship from port P = sqrt((9cos32 + 6)^2 + (9sin32)^2) = 14.44 miles from Port P