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Popular Trigonometry >

15.8*sin(30x-90)+5=17

Solution

15.8 \cdot sin (30 x - 90) + 5 = 17

Solution

x = 3 + \frac{πn}{15} + \frac{0.86253 \dots}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{0.86253 \dots}{30} + 3

Degrees

x = 173.53465 \dots^{\circ} + 1 2^{\circ} n, x = 176.24001 \dots^{\circ} + 1 2^{\circ} n

Solution steps

15.8 sin (30 x - 90) + 5 = 17

Multiply both sides by

10

15.8 sin (30 x - 90) + 5 = 17

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

15.8 sin (30 x - 90) \cdot 10 + 5 \cdot 10 = 17 \cdot 10

Refine

158 sin (30 x - 90) + 50 = 170

158 sin (30 x - 90) + 50 = 170

Move

50

to the right side

158 sin (30 x - 90) + 50 = 170

Subtract

50

from both sides

158 sin (30 x - 90) + 50 - 50 = 170 - 50

Simplify

158 sin (30 x - 90) = 120

158 sin (30 x - 90) = 120

Divide both sides by

158

158 sin (30 x - 90) = 120

Divide both sides by

158

\frac{158 sin ( 30 x - 90 )}{158} = \frac{120}{158}

Simplify

sin (30 x - 90) = \frac{60}{79}

sin (30 x - 90) = \frac{60}{79}

Apply trig inverse properties

sin (30 x - 90) = \frac{60}{79}

General solutions for

sin (30 x - 90) = \frac{60}{79}

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

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn, 30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn, 30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

Solve

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn : x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn

Move

90

to the right side

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn

Add

90

to both sides

30 x - 90 + 90 = arcsin (\frac{60}{79}) + 2 πn + 90

Simplify

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

Divide both sides by

30

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

Divide both sides by

30

\frac{30 x}{30} = \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Simplify

\frac{30 x}{30} = \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Simplify

\frac{30 x}{30} : x

\frac{30 x}{30}

Divide the numbers:

\frac{30}{30} = 1

= x

Simplify

\frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30} : 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

\frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Group like terms

= \frac{90}{30} + \frac{2 πn}{30} + \frac{arcsin ( \frac{60}{79} )}{30}

Divide the numbers:

\frac{90}{30} = 3

= 3 + \frac{2 πn}{30} + \frac{arcsin ( \frac{60}{79} )}{30}

Cancel

\frac{2 πn}{30} : \frac{πn}{15}

\frac{2 πn}{30}

Cancel the common factor:

2

= \frac{πn}{15}

= 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

Solve

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn : x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

Move

90

to the right side

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

Add

90

to both sides

30 x - 90 + 90 = π - arcsin (\frac{60}{79}) + 2 πn + 90

Simplify

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

Divide both sides by

30

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

Divide both sides by

30

\frac{30 x}{30} = \frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Simplify

\frac{30 x}{30} = \frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Simplify

\frac{30 x}{30} : x

\frac{30 x}{30}

Divide the numbers:

\frac{30}{30} = 1

= x

Simplify

\frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30} : \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

\frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

Group like terms

= \frac{π}{30} + \frac{90}{30} + \frac{2 πn}{30} - \frac{arcsin ( \frac{60}{79} )}{30}

Divide the numbers:

\frac{90}{30} = 3

= \frac{π}{30} + 3 + \frac{2 πn}{30} - \frac{arcsin ( \frac{60}{79} )}{30}

Cancel

\frac{2 πn}{30} : \frac{πn}{15}

\frac{2 πn}{30}

Cancel the common factor:

2

= \frac{πn}{15}

= \frac{π}{30} + 3 + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30}

Group like terms

= \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

Show solutions in decimal form

x = 3 + \frac{πn}{15} + \frac{0.86253 \dots}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{0.86253 \dots}{30} + 3

Graph

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