What is the general solution for cos(pi/6 t)=cos(pi/6 (t-3)) ?

The general solution for cos(pi/6 t)=cos(pi/6 (t-3)) is t=12n+3/2 ,t= 15/2+12n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(pi/6 t)=cos(pi/6 (t-3))

cos (\frac{π}{6} t) = cos (\frac{π}{6} (t - 3))

t = 12 n + \frac{3}{2}, t = \frac{15}{2} + 12 n

Solution steps

cos (\frac{π}{6} t) = cos (\frac{π}{6} (t - 3))

Subtract

cos (\frac{π}{6} (t - 3))

from both sides

cos (\frac{π t}{6}) - cos (\frac{π}{6} (t - 3)) = 0

Simplify

cos (\frac{π t}{6}) - cos (\frac{π}{6} (t - 3)) : cos (\frac{π t}{6}) - cos (\frac{π ( t - 3 )}{6})

cos (\frac{π t}{6}) - cos (\frac{π ( t - 3 )}{6}) = 0

Rewrite using trig identities

- 2 sin (\frac{2 π t - 3 π}{12}) = 0

Divide both sides by

- 2

sin (\frac{2 π t - 3 π}{12}) = 0

General solutions for

sin (\frac{2 π t - 3 π}{12}) = 0

\frac{2 π t - 3 π}{12} = 0 + 2 πn, \frac{2 π t - 3 π}{12} = π + 2 πn

Solve

\frac{2 π t - 3 π}{12} = 0 + 2 πn : t = 12 n + \frac{3}{2}

Solve

\frac{2 π t - 3 π}{12} = π + 2 πn : t = \frac{15}{2} + 12 n

t = 12 n + \frac{3}{2}, t = \frac{15}{2} + 12 n

0 = arcsin (x)

cos (2 y) - sin (2 y) = 0

sec (\frac{2 π}{3} + x) = 2

sin (t) = \frac{7}{9}, sin (2 t)

\frac{8}{17} = sin (2 x)

What is the general solution for cos(pi/6 t)=cos(pi/6 (t-3)) ?
The general solution for cos(pi/6 t)=cos(pi/6 (t-3)) is t=12n+3/2 ,t= 15/2+12n