What is the general solution for -6sin(x)-4sin(2x)=0 ?

The general solution for -6sin(x)-4sin(2x)=0 is x=2pin,x=pi+2pin,x=2.41885…+2pin,x=-2.41885…+2pin

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-6sin(x)-4sin(2x)=0

- 6 sin (x) - 4 sin (2 x) = 0

x = 2 πn, x = π + 2 πn, x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

Solution steps

- 6 sin (x) - 4 sin (2 x) = 0

Rewrite using trig identities

- 6 sin (x) - 8 cos (x) sin (x) = 0

Factor

- 6 sin (x) - 8 cos (x) sin (x) : - 2 sin (x) (4 cos (x) + 3)

- 2 sin (x) (4 cos (x) + 3) = 0

Solving each part separately

sin (x) = 0 or 4 cos (x) + 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos (x) + 3 = 0 : x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

t, x = 2 cos (t)

6 sin (θ) = 2.5 cos (θ)

tan^{3} (x) + tan^{2} (x) - tan (x) - 1 = 0

tan (θ) = \frac{- 4 3}{4}

3 sin (x) - cos (x) = 3, 0 \leq x \leq 2 π

What is the general solution for -6sin(x)-4sin(2x)=0 ?
The general solution for -6sin(x)-4sin(2x)=0 is x=2pin,x=pi+2pin,x=2.41885…+2pin,x=-2.41885…+2pin