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

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

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3sin(x)-2=-2

3 sin (x) - 2 = - 2

x = 2 πn, x = π + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

3 sin (x) - 2 = - 2

Add

2

to both sides

3 sin (x) - 2 + 2 = - 2 + 2

Simplify

3 sin (x) = 0

Divide both sides by

3

3 sin (x) = 0

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{0}{3}

Simplify

sin (x) = 0

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

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

4 sin (x^{\circ}) + 1 = - 2

(2 cos (x) + 1) (3 tan (x) - 1) = 0

α, cos^{2} (α) + cos^{2} (β) = 1

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

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