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Popular Trigonometry >

20=2.891sin(0.016d-1.183)+18.512

Solution

20 = 2.891 sin (0.016 d - 1.183) + 18.512

Solution

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Degrees

d = 6172.39781 \dots^{\circ} + 2250 0^{\circ} n, d = 13550.21558 \dots^{\circ} + 2250 0^{\circ} n

Solution steps

20 = 2.891 sin (0.016 d - 1.183) + 18.512

Switch sides

2.891 sin (0.016 d - 1.183) + 18.512 = 20

Multiply both sides by

1000

2.891 sin (0.016 d - 1.183) + 18.512 = 20

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

2.891 sin (0.016 d - 1.183) \cdot 1000 + 18.512 \cdot 1000 = 20 \cdot 1000

Refine

2891 sin (0.016 d - 1.183) + 18512 = 20000

2891 sin (0.016 d - 1.183) + 18512 = 20000

Move

18512

to the right side

2891 sin (0.016 d - 1.183) + 18512 = 20000

Subtract

18512

from both sides

2891 sin (0.016 d - 1.183) + 18512 - 18512 = 20000 - 18512

Simplify

2891 sin (0.016 d - 1.183) = 1488

2891 sin (0.016 d - 1.183) = 1488

Divide both sides by

2891

2891 sin (0.016 d - 1.183) = 1488

Divide both sides by

2891

\frac{2891 sin ( 0.016 d - 1.183 )}{2891} = \frac{1488}{2891}

Simplify

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891}

Apply trig inverse properties

sin (0.016 d - 1.183) = \frac{1488}{2891}

General solutions for

sin (0.016 d - 1.183) = \frac{1488}{2891}

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

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Solve

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

Move

1.183

to the right side

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

Add

1.183

to both sides

0.016 d - 1.183 + 1.183 = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Simplify

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Divide both sides by

0.016

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Divide both sides by

0.016

\frac{0.016 d}{0.016} = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Simplify

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Solve

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Move

1.183

to the right side

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

Add

1.183

to both sides

0.016 d - 1.183 + 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Simplify

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Divide both sides by

0.016

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

Divide both sides by

0.016

\frac{0.016 d}{0.016} = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Simplify

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Show solutions in decimal form

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

Graph

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