-sin^3(t)+sin(2t)cos(t)=0

Solution

- sin^{3} (t) + sin (2 t) cos (t) = 0

t = 2 πn, t = π + 2 πn, t = - 0.95531 \dots + πn, t = 0.95531 \dots + πn

Solution steps

- sin^{3} (t) + sin (2 t) cos (t) = 0

Rewrite using trig identities

- sin^{3} (t) + 2 cos^{2} (t) sin (t) = 0

Factor

- sin^{3} (t) + 2 cos^{2} (t) sin (t) : sin (t) (2 cos (t) + sin (t)) (2 cos (t) - sin (t))

sin (t) (2 cos (t) + sin (t)) (2 cos (t) - sin (t)) = 0

Solving each part separately

sin (t) = 0 or 2 cos (t) + sin (t) = 0 or 2 cos (t) - sin (t) = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

2 cos (t) + sin (t) = 0 : t = arctan (- 2) + πn

2 cos (t) - sin (t) = 0 : t = arctan (2) + πn

Combine all the solutions

t = 2 πn, t = π + 2 πn, t = arctan (- 2) + πn, t = arctan (2) + πn

Show solutions in decimal form

t = 2 πn, t = π + 2 πn, t = - 0.95531 \dots + πn, t = 0.95531 \dots + πn

tan (θ) = 3 tan (4 5^{\circ})

- cot (x) csc (x) = 0

2 cos (2 θ) - 3 cos (θ) - 5 = - 7

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

cos (3 x + π) = \frac{2}{2}