What is the general solution for sin(2x+30)=0.8 ?

The general solution for sin(2x+30)=0.8 is x=-15+pin+(0.92729…)/2 ,x=pin+pi/2-(0.92729…)/2-15

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Popular Trigonometry >

sin(2x+30)=0.8

Solution

sin (2 x + 30) = 0.8

Solution

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

Degrees

x = - 832.87164 \dots^{\circ} + 18 0^{\circ} n, x = - 796.00174 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x + 30) = 0.8

Apply trig inverse properties

sin (2 x + 30) = 0.8

General solutions for

sin (2 x + 30) = 0.8

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

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

Solve

2 x + 30 = arcsin (0.8) + 2 πn : x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

2 x + 30 = arcsin (0.8) + 2 πn

Move

30

to the right side

2 x + 30 = arcsin (0.8) + 2 πn

Subtract

30

from both sides

2 x + 30 - 30 = arcsin (0.8) + 2 πn - 30

Simplify

2 x = arcsin (0.8) + 2 πn - 30

2 x = arcsin (0.8) + 2 πn - 30

Divide both sides by

2

2 x = arcsin (0.8) + 2 πn - 30

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplify

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : - 15 + πn + \frac{arcsin ( 0.8 )}{2}

\frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Group like terms

= - \frac{30}{2} + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

Divide the numbers:

\frac{30}{2} = 15

= - 15 + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

Solve

2 x + 30 = π - arcsin (0.8) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

2 x + 30 = π - arcsin (0.8) + 2 πn

Move

30

to the right side

2 x + 30 = π - arcsin (0.8) + 2 πn

Subtract

30

from both sides

2 x + 30 - 30 = π - arcsin (0.8) + 2 πn - 30

Simplify

2 x = π - arcsin (0.8) + 2 πn - 30

2 x = π - arcsin (0.8) + 2 πn - 30

Divide both sides by

2

2 x = π - arcsin (0.8) + 2 πn - 30

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Simplify

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{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 ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

\frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

Group like terms

= \frac{π}{2} - \frac{30}{2} + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

Divide the numbers:

\frac{30}{2} = 15

= \frac{π}{2} - 15 + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} - 15 + πn - \frac{arcsin ( 0.8 )}{2}

Group like terms

= πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

Show solutions in decimal form

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sin(2x+30)=0.8 ?
The general solution for sin(2x+30)=0.8 is x=-15+pin+(0.92729…)/2 ,x=pin+pi/2-(0.92729…)/2-15