What is the general solution for -3sin(x)-2cos(2x)=0 ?

The general solution for -3sin(x)-2cos(2x)=0 is x=-0.43939…+2pin,x=pi+0.43939…+2pin

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

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

x = - 0.43939 \dots + 2 πn, x = π + 0.43939 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

- (1 - 2 sin^{2} (x)) \cdot 2 - 3 sin (x) = 0

Solve by substitution

sin (x) = \frac{3 + 41}{8}, sin (x) = \frac{3 - 41}{8}

sin (x) = \frac{3 + 41}{8} :

No Solution

sin (x) = \frac{3 - 41}{8} : x = arcsin (\frac{3 - 41}{8}) + 2 πn, x = π + arcsin (- \frac{3 - 41}{8}) + 2 πn

Combine all the solutions

x = arcsin (\frac{3 - 41}{8}) + 2 πn, x = π + arcsin (- \frac{3 - 41}{8}) + 2 πn

Show solutions in decimal form

x = - 0.43939 \dots + 2 πn, x = π + 0.43939 \dots + 2 πn

2 cos (x) tan (x) = 1

sin (10 x) = sin (7 x)

185 = \frac{220 2}{π} - cos (π) + cos (x)

x, 2 sin^{2} (x) = sin (x)

3 cos^{2} (θ) - 2 sin (θ) = 1

What is the general solution for -3sin(x)-2cos(2x)=0 ?
The general solution for -3sin(x)-2cos(2x)=0 is x=-0.43939…+2pin,x=pi+0.43939…+2pin