What is the general solution for 3(1-sin(θ))=2cos^2(θ) ?

The general solution for 3(1-sin(θ))=2cos^2(θ) is θ= pi/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3(1-sin(θ))=2cos^2(θ)

3 (1 - sin (θ)) = 2 cos^{2} (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

3 (1 - sin (θ)) = 2 cos^{2} (θ)

Subtract

2 cos^{2} (θ)

from both sides

3 (1 - sin (θ)) - 2 cos^{2} (θ) = 0

Rewrite using trig identities

1 + 2 sin^{2} (θ) - 3 sin (θ) = 0

Solve by substitution

sin (θ) = 1, sin (θ) = \frac{1}{2}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (x) = \frac{5}{5}

tan (θ) = 0.11246

cos (2 θ) - sin^{2} (θ) = 1

sin (x) = \frac{3}{4}

2 sin (2 x) = 3 sin (x)

What is the general solution for 3(1-sin(θ))=2cos^2(θ) ?
The general solution for 3(1-sin(θ))=2cos^2(θ) is θ= pi/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin