What is the general solution for -2sin(2x)= pi/(12) ?

The general solution for -2sin(2x)= pi/(12) is x=-(0.13127…)/2+pin,x= pi/2+(0.13127…)/2+pin

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-2sin(2x)= pi/(12)

Solution

- 2 sin (2 x) = \frac{π}{12}

Solution

x = - \frac{0.13127 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.13127 \dots}{2} + πn

Degrees

x = - 3.76079 \dots^{\circ} + 18 0^{\circ} n, x = 93.76079 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 2 sin (2 x) = \frac{π}{12}

Divide both sides by

- 2

- 2 sin (2 x) = \frac{π}{12}

Divide both sides by

- 2

\frac{- 2 sin ( 2 x )}{- 2} = \frac{\frac{π}{12}}{- 2}

Simplify

\frac{- 2 sin ( 2 x )}{- 2} = \frac{\frac{π}{12}}{- 2}

Simplify

\frac{- 2 sin ( 2 x )}{- 2} : sin (2 x)

\frac{- 2 sin ( 2 x )}{- 2}

Apply the fraction rule:

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

= \frac{2 sin ( 2 x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (2 x)

Simplify

\frac{\frac{π}{12}}{- 2} : - \frac{π}{24}

\frac{\frac{π}{12}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{π}{12}}{2}

Apply the fraction rule:

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

\frac{\frac{π}{12}}{2} = \frac{π}{12 \cdot 2}

= - \frac{π}{12 \cdot 2}

Multiply the numbers:

12 \cdot 2 = 24

= - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

Apply trig inverse properties

sin (2 x) = - \frac{π}{24}

General solutions for

sin (2 x) = - \frac{π}{24}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

2 x = arcsin (- \frac{π}{24}) + 2 πn, 2 x = π + arcsin (\frac{π}{24}) + 2 πn

2 x = arcsin (- \frac{π}{24}) + 2 πn, 2 x = π + arcsin (\frac{π}{24}) + 2 πn

Solve

2 x = arcsin (- \frac{π}{24}) + 2 πn : x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

2 x = arcsin (- \frac{π}{24}) + 2 πn

Simplify

arcsin (- \frac{π}{24}) + 2 πn : - arcsin (\frac{π}{24}) + 2 πn

arcsin (- \frac{π}{24}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{π}{24}) = - arcsin (\frac{π}{24})

= - arcsin (\frac{π}{24}) + 2 πn

2 x = - arcsin (\frac{π}{24}) + 2 πn

Divide both sides by

2

2 x = - arcsin (\frac{π}{24}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{π}{24} )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

Solve

2 x = π + arcsin (\frac{π}{24}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

2 x = π + arcsin (\frac{π}{24}) + 2 πn

Divide both sides by

2

2 x = π + arcsin (\frac{π}{24}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

Show solutions in decimal form

x = - \frac{0.13127 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.13127 \dots}{2} + πn

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cos (x) = \frac{sec ( x )}{4}

sin(10x)=sin(10(x+1))

sin (10 x) = sin (10 (x + 1))

sin^2(θ)+3sin(θ)=0

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1.04cos^2(x)+0.102cos(x)-0.935=0

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Frequently Asked Questions (FAQ)

What is the general solution for -2sin(2x)= pi/(12) ?
The general solution for -2sin(2x)= pi/(12) is x=-(0.13127…)/2+pin,x= pi/2+(0.13127…)/2+pin