What is the general solution for 3sin(x)+1=0 ?

The general solution for 3sin(x)+1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin

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3sin(x)+1=0

3 sin (x) + 1 = 0

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

Degrees

x = - 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 199.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 sin (x) + 1 = 0

Move

1

to the right side

3 sin (x) + 1 = 0

Subtract

1

from both sides

3 sin (x) + 1 - 1 = 0 - 1

Simplify

3 sin (x) = - 1

3 sin (x) = - 1

Divide both sides by

3

3 sin (x) = - 1

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{- 1}{3}

Simplify

sin (x) = - \frac{1}{3}

sin (x) = - \frac{1}{3}

Apply trig inverse properties

sin (x) = - \frac{1}{3}

General solutions for

sin (x) = - \frac{1}{3}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

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

cot (θ) = - \frac{1}{3}

32 cos (θ) + 3 = 6

- 8 cos (θ) - 4 = - 4

2 cot (x) = 0

What is the general solution for 3sin(x)+1=0 ?
The general solution for 3sin(x)+1=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin