sin^3(x)-0.25sin(x)=0

Solution

sin^{3} (x) - 0.25 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

sin^{3} (x) - 0.25 sin (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - 0.5, sin (x) = 0.5

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 0.5 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 0.5 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin^{2} (x) cos (x) = 0

sin (x) - cos (x) = \frac{3}{2}

cos (x) = \frac{1 - cos ( x )}{2}

csc (x) = \frac{7}{4}

2 - 4 cos (A) = 0