What is the general solution for sin(x)a= pi/3 ?

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

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sin(x)a= pi/3

sin (x) a = \frac{π}{3}

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

Solution steps

sin (x) a = \frac{π}{3}

Divide both sides by

a; a \neq = 0

sin (x) a = \frac{π}{3}

Divide both sides by

a; a \neq = 0

\frac{sin ( x ) a}{a} = \frac{\frac{π}{3}}{a}; a \neq = 0

Simplify

\frac{sin ( x ) a}{a} = \frac{\frac{π}{3}}{a}

Simplify

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

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

Cancel the common factor:

a

= sin (x)

Simplify

\frac{\frac{π}{3}}{a} : \frac{π}{3 a}

\frac{\frac{π}{3}}{a}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 a}

sin (x) = \frac{π}{3 a}; a \neq = 0

sin (x) = \frac{π}{3 a}; a \neq = 0

sin (x) = \frac{π}{3 a}; a \neq = 0

Apply trig inverse properties

sin (x) = \frac{π}{3 a}

General solutions for

sin (x) = \frac{π}{3 a}

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

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

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

cos (θ) = \frac{6}{14 \cdot 9}

sin (θ + \frac{π}{4}) = \frac{1}{2}

(cot (x) - 1) (sin (x) - 1) = 0

so l v e f or x, u = cos (x)

cos (2 x) = \frac{119}{169}

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