What is the general solution for cos^3(t)=cos(t) ?

The general solution for cos^3(t)=cos(t) is t= pi/2+2pin,t=(3pi)/2+2pin,t=pi+2pin,t=2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^3(t)=cos(t)

cos^{3} (t) = cos (t)

t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn, t = π + 2 πn, t = 2 πn

Solution steps

cos^{3} (t) = cos (t)

Solve by substitution

cos (t) = 0, cos (t) = - 1, cos (t) = 1

cos (t) = 0 : t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

cos (t) = - 1 : t = π + 2 πn

cos (t) = 1 : t = 2 πn

Combine all the solutions

t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn, t = π + 2 πn, t = 2 πn

sec (x) = 4

2 sin^{2} (x) - 3 sin (x) = 0

sin (x) sin (2 x) - cos (x) cos (2 x) = \frac{3}{2}

sec (x) - tan (x) = cos (x)

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

What is the general solution for cos^3(t)=cos(t) ?
The general solution for cos^3(t)=cos(t) is t= pi/2+2pin,t=(3pi)/2+2pin,t=pi+2pin,t=2pin