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

The general solution for sqrt(3)sin(x)+1=0 is x=-0.61547…+2pin,x=pi+0.61547…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

3 sin (x) + 1 = 0

x = - 0.61547 \dots + 2 πn, x = π + 0.61547 \dots + 2 πn

Degrees

x = - 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 215.26438 \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

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

Simplify

\frac{3 sin ( x )}{3} : sin (x)

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

Cancel the common factor:

3

= sin (x)

Simplify

\frac{- 1}{3} : - \frac{3}{3}

\frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = - 0.61547 \dots + 2 πn, x = π + 0.61547 \dots + 2 πn

sin (y) = \frac{1}{2}

tan (2 θ) = 2.93

cot (θ + 1) csc (θ - 1) = 0

sin (a) = 0.9455

x, \frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

What is the general solution for sqrt(3)sin(x)+1=0 ?
The general solution for sqrt(3)sin(x)+1=0 is x=-0.61547…+2pin,x=pi+0.61547…+2pin