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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor t,x=cos(2t)

solve for

t, x = cos (2 t)

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

Solution steps

x = cos (2 t)

Switch sides

cos (2 t) = x

Apply trig inverse properties

cos (2 t) = x

General solutions for

cos (2 t) = x

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

2 t = arccos (x) + 2 πn, 2 t = - arccos (x) + 2 πn

2 t = arccos (x) + 2 πn, 2 t = - arccos (x) + 2 πn

Solve

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

2 t = arccos (x) + 2 πn

Divide both sides by

2

2 t = arccos (x) + 2 πn

Divide both sides by

2

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

Simplify

t = \frac{arccos ( x )}{2} + πn

t = \frac{arccos ( x )}{2} + πn

Solve

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

2 t = - arccos (x) + 2 πn

Divide both sides by

2

2 t = - arccos (x) + 2 πn

Divide both sides by

2

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

Simplify

t = - \frac{arccos ( x )}{2} + πn

t = - \frac{arccos ( x )}{2} + πn

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

- 9 sin^{2} (θ) - 3 cos (θ) + 2 = - 5

csc (x) = - 1 + cot (x)

2 sin (3 x) = 3

4 sin (3 θ) = 7 cos (3 θ), 0^{\circ} \leq 3 θ < 72 0^{\circ}

cot (θ) = 4

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