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Popular Trigonometry >

15=10sin(pi/(20)(x+10))+12

Solution

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

Solution

x = \frac{20 \cdot 0.30469 \dots}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 \cdot 0.30469 \dots}{π}

Degrees

x = - 461.81924 \dots^{\circ} + 2291.83118 \dots^{\circ} n, x = 461.81924 \dots^{\circ} + 2291.83118 \dots^{\circ} n

Solution steps

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

Switch sides

10 sin (\frac{π}{20} (x + 10)) + 12 = 15

Move

12

to the right side

10 sin (\frac{π}{20} (x + 10)) + 12 = 15

Subtract

12

from both sides

10 sin (\frac{π}{20} (x + 10)) + 12 - 12 = 15 - 12

Simplify

10 sin (\frac{π}{20} (x + 10)) = 3

10 sin (\frac{π}{20} (x + 10)) = 3

Divide both sides by

10

10 sin (\frac{π}{20} (x + 10)) = 3

Divide both sides by

10

\frac{10 sin ( \frac{π}{20} ( x + 10 ) )}{10} = \frac{3}{10}

Simplify

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

Apply trig inverse properties

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

General solutions for

sin (\frac{π}{20} (x + 10)) = \frac{3}{10}

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

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn, \frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn, \frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Solve

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn : x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn

Multiply both sides by

20

\frac{π}{20} (x + 10) = arcsin (\frac{3}{10}) + 2 πn

Multiply both sides by

20

20 \cdot \frac{π}{20} (x + 10) = 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplify

20 \cdot \frac{π}{20} (x + 10) = 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplify

20 \cdot \frac{π}{20} (x + 10) : π (x + 10)

20 \cdot \frac{π}{20} (x + 10)

Multiply fractions:

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

= \frac{20 π}{20} (x + 10)

Cancel the common factor:

20

= (x + 10) π

Simplify

20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn : 20 arcsin (\frac{3}{10}) + 40 πn

20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Multiply the numbers:

20 \cdot 2 = 40

= 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

Divide both sides by

π

π (x + 10) = 20 arcsin (\frac{3}{10}) + 40 πn

Divide both sides by

π

\frac{π ( x + 10 )}{π} = \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplify

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Move

10

to the right side

x + 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Subtract

10

from both sides

x + 10 - 10 = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplify

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Solve

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn : x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Multiply both sides by

20

\frac{π}{20} (x + 10) = π - arcsin (\frac{3}{10}) + 2 πn

Multiply both sides by

20

20 \cdot \frac{π}{20} (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplify

20 \cdot \frac{π}{20} (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Simplify

20 \cdot \frac{π}{20} (x + 10) : π (x + 10)

20 \cdot \frac{π}{20} (x + 10)

Multiply fractions:

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

= \frac{20 π}{20} (x + 10)

Cancel the common factor:

20

= (x + 10) π

Simplify

20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn : 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

20 π - 20 arcsin (\frac{3}{10}) + 20 \cdot 2 πn

Multiply the numbers:

20 \cdot 2 = 40

= 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

Divide both sides by

π

π (x + 10) = 20 π - 20 arcsin (\frac{3}{10}) + 40 πn

Divide both sides by

π

\frac{π ( x + 10 )}{π} = \frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplify

\frac{π ( x + 10 )}{π} = \frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Simplify

\frac{π ( x + 10 )}{π} : x + 10

\frac{π ( x + 10 )}{π}

Cancel the common factor:

π

= x + 10

Simplify

\frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π} : 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

\frac{20 π}{π} - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Cancel

\frac{20 π}{π} : 20

\frac{20 π}{π}

Cancel the common factor:

π

= 20

= 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + \frac{40 πn}{π}

Cancel

\frac{40 πn}{π} : 40 n

\frac{40 πn}{π}

Cancel the common factor:

π

= 40 n

= 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Move

10

to the right side

x + 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n

Subtract

10

from both sides

x + 10 - 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplify

x + 10 - 10 = 20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Simplify

x + 10 - 10 : x

x + 10 - 10

Add similar elements:

10 - 10 = 0

= x

Simplify

20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10 : 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

20 - \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10

Subtract the numbers:

20 - 10 = 10

= 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

x = \frac{20 arcsin ( \frac{3}{10} )}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 arcsin ( \frac{3}{10} )}{π}

Show solutions in decimal form

x = \frac{20 \cdot 0.30469 \dots}{π} + 40 n - 10, x = 40 n + 10 - \frac{20 \cdot 0.30469 \dots}{π}

Graph

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