Examples Double Angle Formulas Find the exact value of the trig function. 5 1) sin x 3 x 4 2) cos x x = 4 y = 3 r = 5 3) tan x

Examples Double Angle Formulas 5 Find the exact value of the trig function. 3 x -4 4) sin 2x x = -4 y = 3 r = 5 5) cos 2x 6) tan 2x

Examples Double Angle Formulas Find the exact value of the equation in the interval [0 , 2π). 7) sin 2x + cos x = 0 8) sin 2x sin x = cos x (2 sin x cos x) + cos x = 0 (2 sin x cos x) sin x = cos x cos x (2 sin x + 1) = 0 2 sin 2 x cos x - cos x = 0 cos x = 0 2 sin x + 1 = 0 cos x ( 2 sin 2 x - 1) = 0 sin x = -1/2 cos x = 0 2 sin 2 x - 1 = 0 sin 2 x = 1/2 sin x =

Examples Double Angle Formulas Find the exact value of the equation in the interval [0 , 2π). 9) cos 2x + sin x = 0 1 - 2 sin 2 x + sin x = 0 write in standard form and change all the signs (multiply by -1) to make sin2x a positive # . 2 sin 2 x - sin x - 1 = 0 think of this as 2x2 - x - 1 and factor (2x + 1) (x - 1) Now put the sin x back in. (2 sin x + 1) (sin x - 1) = 0 2 sin x + 1 = 0 sin x - 1 = 0 sin x = -1/2 sin x = 1