sin(x)(2sin^2(x)-1)=0

Solution

sin (x) (2 sin^{2} (x) - 1) = 0

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

sin (x) (2 sin^{2} (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 2 sin^{2} (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 sin^{2} (x) - 1 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (2 x) = 10 cos (x)

- 2 cos (3 θ) = 1, 0 \leq θ \leq 2 π

cos (a) = 0.998482

3 - 4 sin (θ) = 4 - 6 sin (θ)

\frac{cos ( x )}{sin ( x )} = - 0.00172