What is the general solution for solvefor t,x=2cos(t) ?

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

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solvefor t,x=2cos(t)

solve for

t, x = 2 cos (t)

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

Solution steps

x = 2 cos (t)

Switch sides

2 cos (t) = x

Divide both sides by

2

2 cos (t) = x

Divide both sides by

2

\frac{2 cos ( t )}{2} = \frac{x}{2}

Simplify

cos (t) = \frac{x}{2}

cos (t) = \frac{x}{2}

Apply trig inverse properties

cos (t) = \frac{x}{2}

General solutions for

cos (t) = \frac{x}{2}

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

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

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

6 sin (θ) = 2.5 cos (θ)

tan^{3} (x) + tan^{2} (x) - tan (x) - 1 = 0

tan (θ) = \frac{- 4 3}{4}

3 sin (x) - cos (x) = 3, 0 \leq x \leq 2 π

- 1 + 3 sin (x) = - 1 + 4 sin (x)

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