What is the general solution for sin(x)a= pi/2 ?

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

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sin(x)a= pi/2

sin (x) a = \frac{π}{2}

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

Solution steps

sin (x) a = \frac{π}{2}

Divide both sides by

a; a \neq = 0

sin (x) a = \frac{π}{2}

Divide both sides by

a; a \neq = 0

\frac{sin ( x ) a}{a} = \frac{\frac{π}{2}}{a}; a \neq = 0

Simplify

\frac{sin ( x ) a}{a} = \frac{\frac{π}{2}}{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}{2}}{a} : \frac{π}{2 a}

\frac{\frac{π}{2}}{a}

Apply the fraction rule:

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

= \frac{π}{2 a}

sin (x) = \frac{π}{2 a}; a \neq = 0

sin (x) = \frac{π}{2 a}; a \neq = 0

sin (x) = \frac{π}{2 a}; a \neq = 0

Apply trig inverse properties

sin (x) = \frac{π}{2 a}

General solutions for

sin (x) = \frac{π}{2 a}

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

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

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

tan^{2} (3 θ) = 1

tan^{2} (2 θ) - 3 = 0

cos (2 x) = 5 sin^{2} (x) - cos^{2} (x)

3 sec (5 x) - 2 = 0

cot^{2} (x) sec (x) - sec (x) = 2 cot^{2} (x) - 2

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