What is the general solution for ksin(x)-c=0 ?

The general solution for ksin(x)-c=0 is x=arcsin(c/k)+2pin,x=pi+arcsin(-c/k)+2pin

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ksin(x)-c=0

k sin (x) - c = 0

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

Solution steps

k sin (x) - c = 0

Move

c

to the right side

k sin (x) - c = 0

Add

c

to both sides

k sin (x) - c + c = 0 + c

Simplify

k sin (x) = c

k sin (x) = c

Divide both sides by

k; k \neq = 0

k sin (x) = c

Divide both sides by

k; k \neq = 0

\frac{k sin ( x )}{k} = \frac{c}{k}; k \neq = 0

Simplify

sin (x) = \frac{c}{k}; k \neq = 0

sin (x) = \frac{c}{k}; k \neq = 0

Apply trig inverse properties

sin (x) = \frac{c}{k}

General solutions for

sin (x) = \frac{c}{k}

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

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

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

cos (x) = sin (x - \frac{π}{2})

5 cos (x) + 2 = 0, 0 \leq x \leq 2 π

2 sin (x) cos (x) - sin (2 x) cos (2 x) = 0

cos (x) = \frac{21}{29}

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

What is the general solution for ksin(x)-c=0 ?
The general solution for ksin(x)-c=0 is x=arcsin(c/k)+2pin,x=pi+arcsin(-c/k)+2pin