What is the general solution for solvefor t,x=3cos(t) ?

The general solution for solvefor t,x=3cos(t) is t=arccos(x/3)+2pin,t=-arccos(x/3)+2pin

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solvefor t,x=3cos(t)

solve for

t, x = 3 cos (t)

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

Solution steps

x = 3 cos (t)

Switch sides

3 cos (t) = x

Divide both sides by

3

3 cos (t) = x

Divide both sides by

3

\frac{3 cos ( t )}{3} = \frac{x}{3}

Simplify

cos (t) = \frac{x}{3}

cos (t) = \frac{x}{3}

Apply trig inverse properties

cos (t) = \frac{x}{3}

General solutions for

cos (t) = \frac{x}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

tan^{2} (θ) = - \frac{3}{2} sec (θ), 0 \leq θ < 2 π

5 sin (x) + 3 cos (x) = 0

3 cos (x) csc (x) = 2 cos (x)

sin (2 x) = - \frac{2}{2}

sin (x) = 0, 0 \leq x < 2 π

What is the general solution for solvefor t,x=3cos(t) ?
The general solution for solvefor t,x=3cos(t) is t=arccos(x/3)+2pin,t=-arccos(x/3)+2pin