What is the general solution for -2sqrt(2)=-4sin(2θ) ?

The general solution for -2sqrt(2)=-4sin(2θ) is θ= pi/8+pin,θ=(3pi)/8+pin

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Popular >

-2sqrt(2)=-4sin(2θ)

Solution

- 22 = - 4 sin (2 θ)

Solution

θ = \frac{π}{8} + πn, θ = \frac{3 π}{8} + πn

Degrees

θ = 22. 5^{\circ} + 18 0^{\circ} n, θ = 67. 5^{\circ} + 18 0^{\circ} n

Solution steps

- 22 = - 4 sin (2 θ)

Switch sides

- 4 sin (2 θ) = - 22

Divide both sides by

- 4

- 4 sin (2 θ) = - 22

Divide both sides by

- 4

\frac{- 4 sin ( 2 θ )}{- 4} = \frac{- 2 2}{- 4}

Simplify

\frac{- 4 sin ( 2 θ )}{- 4} = \frac{- 2 2}{- 4}

Simplify

\frac{- 4 sin ( 2 θ )}{- 4} : sin (2 θ)

\frac{- 4 sin ( 2 θ )}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4 sin ( 2 θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (2 θ)

Simplify

\frac{- 2 2}{- 4} : \frac{2}{2}

\frac{- 2 2}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 2}{4}

Cancel the common factor:

2

= \frac{2}{2}

sin (2 θ) = \frac{2}{2}

sin (2 θ) = \frac{2}{2}

sin (2 θ) = \frac{2}{2}

General solutions for

sin (2 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}

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

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

Solve

2 θ = \frac{π}{4} + 2 πn : θ = \frac{π}{8} + πn

2 θ = \frac{π}{4} + 2 πn

Divide both sides by

2

2 θ = \frac{π}{4} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

\frac{\frac{π}{4}}{2} + \frac{2 πn}{2} : \frac{π}{8} + πn

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

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{π}{8} + πn

θ = \frac{π}{8} + πn

θ = \frac{π}{8} + πn

θ = \frac{π}{8} + πn

Solve

2 θ = \frac{3 π}{4} + 2 πn : θ = \frac{3 π}{8} + πn

2 θ = \frac{3 π}{4} + 2 πn

Divide both sides by

2

2 θ = \frac{3 π}{4} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

\frac{\frac{3 π}{4}}{2} + \frac{2 πn}{2} : \frac{3 π}{8} + πn

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

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{3 π}{8} + πn

θ = \frac{3 π}{8} + πn

θ = \frac{3 π}{8} + πn

θ = \frac{3 π}{8} + πn

θ = \frac{π}{8} + πn, θ = \frac{3 π}{8} + πn

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8 cos (x) = 4 cos^{2} (x) + 3

(sin^2(x))/2+c=cos(x)c+c

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

-tan(x)-sec(x)=0

- tan (x) - sec (x) = 0

(26)/(sin(88))=(21)/(sin(c))

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

3tan^2(3x)=1

3 tan^{2} (3 x) = 1

Frequently Asked Questions (FAQ)

What is the general solution for -2sqrt(2)=-4sin(2θ) ?
The general solution for -2sqrt(2)=-4sin(2θ) is θ= pi/8+pin,θ=(3pi)/8+pin