What is the general solution for 6sin(θ)=3+3sin(θ) ?

The general solution for 6sin(θ)=3+3sin(θ) is θ= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6sin(θ)=3+3sin(θ)

6 sin (θ) = 3 + 3 sin (θ)

θ = \frac{π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (θ) = 3 + 3 sin (θ)

Solve by substitution

6 sin (θ) = 3 + 3 sin (θ)

Let:

sin (θ) = u

6 u = 3 + 3 u

6 u = 3 + 3 u : u = 1

6 u = 3 + 3 u

Move

3 u

to the left side

6 u = 3 + 3 u

Subtract

3 u

from both sides

6 u - 3 u = 3 + 3 u - 3 u

Simplify

3 u = 3

3 u = 3

Divide both sides by

3

3 u = 3

Divide both sides by

3

\frac{3 u}{3} = \frac{3}{3}

Simplify

u = 1

u = 1

Substitute back

u = sin (θ)

sin (θ) = 1

sin (θ) = 1

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = 1

General solutions for

sin (θ) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn

sin (θ) = \frac{- 2}{2 2}, 0 \leq θ < 2 π

(sin (θ) + 1) (sin (θ) - 1) = 0

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

cos (θ) = \frac{2 3}{5}

cos (2 x) (sin (x) + \frac{2}{2}) = 0

What is the general solution for 6sin(θ)=3+3sin(θ) ?
The general solution for 6sin(θ)=3+3sin(θ) is θ= pi/2+2pin