What is the general solution for solvefor t,x=4sin(t) ?

The general solution for solvefor t,x=4sin(t) is t=arcsin(x/4)+2pin,t=pi+arcsin(-x/4)+2pin

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solvefor t,x=4sin(t)

solve for

t, x = 4 sin (t)

t = arcsin (\frac{x}{4}) + 2 πn, t = π + arcsin (- \frac{x}{4}) + 2 πn

Solution steps

x = 4 sin (t)

Switch sides

4 sin (t) = x

Divide both sides by

4

4 sin (t) = x

Divide both sides by

4

\frac{4 sin ( t )}{4} = \frac{x}{4}

Simplify

sin (t) = \frac{x}{4}

sin (t) = \frac{x}{4}

Apply trig inverse properties

sin (t) = \frac{x}{4}

General solutions for

sin (t) = \frac{x}{4}

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

t = arcsin (\frac{x}{4}) + 2 πn, t = π + arcsin (- \frac{x}{4}) + 2 πn

t = arcsin (\frac{x}{4}) + 2 πn, t = π + arcsin (- \frac{x}{4}) + 2 πn

sin (2 x) + 1.5 cos (x) = 0

sin (w π) = 0

(1 + cos (x)) (1 - sin (x)) - cos^{2} (x) = 0

cos (x) = - 8

arctan (\frac{18.5}{x}) - arctan (\frac{42.41}{x}) = 21.27

What is the general solution for solvefor t,x=4sin(t) ?
The general solution for solvefor t,x=4sin(t) is t=arcsin(x/4)+2pin,t=pi+arcsin(-x/4)+2pin