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Popular Trigonometry >

12.3=2.3sin(24x)+14.1

Solution

12.3 = 2.3 sin (24 x) + 14.1

Solution

x = - \frac{0.89884 \dots}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{0.89884 \dots}{24} + \frac{πn}{12}

Degrees

x = - 2.14583 \dots^{\circ} + 1 5^{\circ} n, x = 9.64583 \dots^{\circ} + 1 5^{\circ} n

Solution steps

12.3 = 2.3 sin (24 x) + 14.1

Switch sides

2.3 sin (24 x) + 14.1 = 12.3

Multiply both sides by

10

2.3 sin (24 x) + 14.1 = 12.3

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

2.3 sin (24 x) \cdot 10 + 14.1 \cdot 10 = 12.3 \cdot 10

Refine

23 sin (24 x) + 141 = 123

23 sin (24 x) + 141 = 123

Move

141

to the right side

23 sin (24 x) + 141 = 123

Subtract

141

from both sides

23 sin (24 x) + 141 - 141 = 123 - 141

Simplify

23 sin (24 x) = - 18

23 sin (24 x) = - 18

Divide both sides by

23

23 sin (24 x) = - 18

Divide both sides by

23

\frac{23 sin ( 24 x )}{23} = \frac{- 18}{23}

Simplify

sin (24 x) = - \frac{18}{23}

sin (24 x) = - \frac{18}{23}

Apply trig inverse properties

sin (24 x) = - \frac{18}{23}

General solutions for

sin (24 x) = - \frac{18}{23}

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

24 x = arcsin (- \frac{18}{23}) + 2 πn, 24 x = π + arcsin (\frac{18}{23}) + 2 πn

24 x = arcsin (- \frac{18}{23}) + 2 πn, 24 x = π + arcsin (\frac{18}{23}) + 2 πn

Solve

24 x = arcsin (- \frac{18}{23}) + 2 πn : x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

24 x = arcsin (- \frac{18}{23}) + 2 πn

Simplify

arcsin (- \frac{18}{23}) + 2 πn : - arcsin (\frac{18}{23}) + 2 πn

arcsin (- \frac{18}{23}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{18}{23}) = - arcsin (\frac{18}{23})

= - arcsin (\frac{18}{23}) + 2 πn

24 x = - arcsin (\frac{18}{23}) + 2 πn

Divide both sides by

24

24 x = - arcsin (\frac{18}{23}) + 2 πn

Divide both sides by

24

\frac{24 x}{24} = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{2 πn}{24}

Simplify

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

Solve

24 x = π + arcsin (\frac{18}{23}) + 2 πn : x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

24 x = π + arcsin (\frac{18}{23}) + 2 πn

Divide both sides by

24

24 x = π + arcsin (\frac{18}{23}) + 2 πn

Divide both sides by

24

\frac{24 x}{24} = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{2 πn}{24}

Simplify

x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

Show solutions in decimal form

x = - \frac{0.89884 \dots}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{0.89884 \dots}{24} + \frac{πn}{12}

Graph

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