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

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

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1=sqrt(3)sin(x)

1 = 3 sin (x)

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

Degrees

x = 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 144.73561 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 = 3 sin (x)

Switch sides

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}

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}

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

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

3 tan (θ) + 1 = 2 tan (θ)

cos (x) = \frac{18}{25}

sin (x) = - \frac{2}{2}, - π \leq x \leq π

w, s (t) = A e^{- c t} cos (wt + b)

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