What is the general solution for 6sin(θ)-3=0 ?

The general solution for 6sin(θ)-3=0 is 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 >

6sin(θ)-3=0

6 sin (θ) - 3 = 0

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

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (θ) - 3 = 0

Move

3

to the right side

6 sin (θ) - 3 = 0

Add

3

to both sides

6 sin (θ) - 3 + 3 = 0 + 3

Simplify

6 sin (θ) = 3

6 sin (θ) = 3

Divide both sides by

6

6 sin (θ) = 3

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{3}{6}

Simplify

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

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}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

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

cot^{2} (x) - csc (x) = 1

cos (2 x) = - 0.6

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

2 cos (x) = sin (2 x)

sec (θ) + 1 = 0

What is the general solution for 6sin(θ)-3=0 ?
The general solution for 6sin(θ)-3=0 is θ= pi/6+2pin,θ=(5pi)/6+2pin