What is the general solution for 3sin^2(t)=2cos(t)sin(t) ?

The general solution for 3sin^2(t)=2cos(t)sin(t) is t=2pin,t=pi+2pin,t=0.58800…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3sin^2(t)=2cos(t)sin(t)

3 sin^{2} (t) = 2 cos (t) sin (t)

t = 2 πn, t = π + 2 πn, t = 0.58800 \dots + πn

Solution steps

3 sin^{2} (t) = 2 cos (t) sin (t)

Subtract

2 cos (t) sin (t)

from both sides

3 sin^{2} (t) - 2 cos (t) sin (t) = 0

Factor

3 sin^{2} (t) - 2 cos (t) sin (t) : sin (t) (3 sin (t) - 2 cos (t))

sin (t) (3 sin (t) - 2 cos (t)) = 0

Solving each part separately

sin (t) = 0 or 3 sin (t) - 2 cos (t) = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

3 sin (t) - 2 cos (t) = 0 : t = arctan (\frac{2}{3}) + πn

Combine all the solutions

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

Show solutions in decimal form

t = 2 πn, t = π + 2 πn, t = 0.58800 \dots + πn

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = 0

cos (x) (tan (x) + \frac{cos ( x )}{sin ( x )}) = 2

2 cos (2 x) + sin (x) = \frac{1}{2}

2 cos^{2} (x) + cos (x) + 1 = 0

cos^{2} (\frac{x}{2}) - sin^{2} (\frac{x}{2}) = 1 - sin (x)

What is the general solution for 3sin^2(t)=2cos(t)sin(t) ?
The general solution for 3sin^2(t)=2cos(t)sin(t) is t=2pin,t=pi+2pin,t=0.58800…+pin