What is the general solution for 2sin(3θ)=sqrt(2) ?

The general solution for 2sin(3θ)=sqrt(2) is θ= pi/(12)+(2pin)/3 ,θ= pi/4+(2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(3θ)=sqrt(2)

Solution

2 sin (3 θ) = 2

Solution

θ = \frac{π}{12} + \frac{2 πn}{3}, θ = \frac{π}{4} + \frac{2 πn}{3}

Degrees

θ = 1 5^{\circ} + 12 0^{\circ} n, θ = 4 5^{\circ} + 12 0^{\circ} n

Solution steps

2 sin (3 θ) = 2

Divide both sides by

2

2 sin (3 θ) = 2

Divide both sides by

2

\frac{2 sin ( 3 θ )}{2} = \frac{2}{2}

Simplify

sin (3 θ) = \frac{2}{2}

sin (3 θ) = \frac{2}{2}

General solutions for

sin (3 θ) = \frac{2}{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}

3 θ = \frac{π}{4} + 2 πn, 3 θ = \frac{3 π}{4} + 2 πn

3 θ = \frac{π}{4} + 2 πn, 3 θ = \frac{3 π}{4} + 2 πn

Solve

3 θ = \frac{π}{4} + 2 πn : θ = \frac{π}{12} + \frac{2 πn}{3}

3 θ = \frac{π}{4} + 2 πn

Divide both sides by

3

3 θ = \frac{π}{4} + 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3} : \frac{π}{12} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{2 πn}{3}

θ = \frac{π}{12} + \frac{2 πn}{3}

θ = \frac{π}{12} + \frac{2 πn}{3}

θ = \frac{π}{12} + \frac{2 πn}{3}

Solve

3 θ = \frac{3 π}{4} + 2 πn : θ = \frac{π}{4} + \frac{2 πn}{3}

3 θ = \frac{3 π}{4} + 2 πn

Divide both sides by

3

3 θ = \frac{3 π}{4} + 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{3 π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{3 π}{4}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{3 π}{4}}{3} + \frac{2 πn}{3} : \frac{π}{4} + \frac{2 πn}{3}

\frac{\frac{3 π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{3 π}{4}}{3} = \frac{π}{4}

\frac{\frac{3 π}{4}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{3 π}{12}

Cancel the common factor:

3

= \frac{π}{4}

= \frac{π}{4} + \frac{2 πn}{3}

θ = \frac{π}{4} + \frac{2 πn}{3}

θ = \frac{π}{4} + \frac{2 πn}{3}

θ = \frac{π}{4} + \frac{2 πn}{3}

θ = \frac{π}{12} + \frac{2 πn}{3}, θ = \frac{π}{4} + \frac{2 πn}{3}

Popular Examples

cot^2(x)+2cot(x)+1=0

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

(cot(x)+1)(sqrt(3)cot(x)+1)=0

(cot (x) + 1) (3 cot (x) + 1) = 0

sqrt(3)sin(θ)=-cos(θ)

3 sin (θ) = - cos (θ)

-2sin(x)+1=0

- 2 sin (x) + 1 = 0

sin(2θ)=-(sqrt(3))/2 ,0<= θ<= 2pi

sin (2 θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(3θ)=sqrt(2) ?
The general solution for 2sin(3θ)=sqrt(2) is θ= pi/(12)+(2pin)/3 ,θ= pi/4+(2pin)/3