What is the general solution for 2sin(2x+15)= 1/2 ?

The general solution for 2sin(2x+15)= 1/2 is x=pin-15/2+(0.25268…)/2 ,x=pin+pi/2-15/2-(0.25268…)/2

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2sin(2x+15)= 1/2

Solution

2 sin (2 x + 15) = \frac{1}{2}

Solution

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

Degrees

x = - 422.47959 \dots^{\circ} + 18 0^{\circ} n, x = - 346.95710 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (2 x + 15) = \frac{1}{2}

Divide both sides by

2

2 sin (2 x + 15) = \frac{1}{2}

Divide both sides by

2

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 sin ( 2 x + 15 )}{2} : sin (2 x + 15)

\frac{2 sin ( 2 x + 15 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (2 x + 15)

Simplify

\frac{\frac{1}{2}}{2} : \frac{1}{4}

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

Apply trig inverse properties

sin (2 x + 15) = \frac{1}{4}

General solutions for

sin (2 x + 15) = \frac{1}{4}

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

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Solve

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn : x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

Move

15

to the right side

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

Subtract

15

from both sides

2 x + 15 - 15 = arcsin (\frac{1}{4}) + 2 πn - 15

Simplify

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

Divide both sides by

2

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Group like terms

= - \frac{15}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= - \frac{15}{2} + πn + \frac{arcsin ( \frac{1}{4} )}{2}

Group like terms

= πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

Solve

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn : x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Move

15

to the right side

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

Subtract

15

from both sides

2 x + 15 - 15 = π - arcsin (\frac{1}{4}) + 2 πn - 15

Simplify

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

Divide both sides by

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Group like terms

= \frac{π}{2} - \frac{15}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} - \frac{15}{2} + πn - \frac{arcsin ( \frac{1}{4} )}{2}

Group like terms

= πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

Show solutions in decimal form

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(2x+15)= 1/2 ?
The general solution for 2sin(2x+15)= 1/2 is x=pin-15/2+(0.25268…)/2 ,x=pin+pi/2-15/2-(0.25268…)/2