-2/(sqrt(3))cos(3θ)=1,0<= θ<= 2pi

Solution

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

θ = \frac{5 π}{18}, θ = \frac{7 π}{18}, θ = \frac{17 π}{18}, θ = \frac{19 π}{18}, θ = \frac{29 π}{18}, θ = \frac{31 π}{18}

Solution steps

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

Simplify

- \frac{2}{3} : - \frac{2 3}{3}

(- \frac{2 3}{3}) cos (3 θ) = 1

Multiply both sides by

3

- 23 cos (3 θ) = 3

Divide both sides by

- 23

cos (3 θ) = - \frac{3}{2}

General solutions for

cos (3 θ) = - \frac{3}{2}

3 θ = \frac{5 π}{6} + 2 πn, 3 θ = \frac{7 π}{6} + 2 πn

Solve

3 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{18} + \frac{2 πn}{3}

Solve

3 θ = \frac{7 π}{6} + 2 πn : θ = \frac{7 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}, θ = \frac{7 π}{18} + \frac{2 πn}{3}

Solutions for the range

0 \leq θ \leq 2 π

θ = \frac{5 π}{18}, θ = \frac{7 π}{18}, θ = \frac{17 π}{18}, θ = \frac{19 π}{18}, θ = \frac{29 π}{18}, θ = \frac{31 π}{18}

8 (cos (x))^{2} - 6 sin (x) = 3

sin (x) = \frac{- tan ( x )}{2}

2 sin (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

sin (θ) = - \frac{5}{7}

cos (x) sin (x) = sin (x)