What is the general solution for 9.2sin(t)+23.2=14.365 ?

The general solution for 9.2sin(t)+23.2=14.365 is t=-1.28816…+2pin,t=pi+1.28816…+2pin

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Popular Trigonometry >

9.2sin(t)+23.2=14.365

Solution

9.2 sin (t) + 23.2 = 14.365

Solution

t = - 1.28816 \dots + 2 πn, t = π + 1.28816 \dots + 2 πn

Degrees

t = - 73.80665 \dots^{\circ} + 36 0^{\circ} n, t = 253.80665 \dots^{\circ} + 36 0^{\circ} n

Solution steps

9.2 sin (t) + 23.2 = 14.365

Multiply both sides by

1000

9.2 sin (t) + 23.2 = 14.365

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

9.2 sin (t) \cdot 1000 + 23.2 \cdot 1000 = 14.365 \cdot 1000

Refine

9200 sin (t) + 23200 = 14365

9200 sin (t) + 23200 = 14365

Move

23200

to the right side

9200 sin (t) + 23200 = 14365

Subtract

23200

from both sides

9200 sin (t) + 23200 - 23200 = 14365 - 23200

Simplify

9200 sin (t) = - 8835

9200 sin (t) = - 8835

Divide both sides by

9200

9200 sin (t) = - 8835

Divide both sides by

9200

\frac{9200 sin ( t )}{9200} = \frac{- 8835}{9200}

Simplify

\frac{9200 sin ( t )}{9200} = \frac{- 8835}{9200}

Simplify

\frac{9200 sin ( t )}{9200} : sin (t)

\frac{9200 sin ( t )}{9200}

Divide the numbers:

\frac{9200}{9200} = 1

= sin (t)

Simplify

\frac{- 8835}{9200} : - \frac{1767}{1840}

\frac{- 8835}{9200}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{8835}{9200}

Cancel the common factor:

5

= - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

sin (t) = - \frac{1767}{1840}

Apply trig inverse properties

sin (t) = - \frac{1767}{1840}

General solutions for

sin (t) = - \frac{1767}{1840}

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

t = arcsin (- \frac{1767}{1840}) + 2 πn, t = π + arcsin (\frac{1767}{1840}) + 2 πn

t = arcsin (- \frac{1767}{1840}) + 2 πn, t = π + arcsin (\frac{1767}{1840}) + 2 πn

Show solutions in decimal form

t = - 1.28816 \dots + 2 πn, t = π + 1.28816 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 9.2sin(t)+23.2=14.365 ?
The general solution for 9.2sin(t)+23.2=14.365 is t=-1.28816…+2pin,t=pi+1.28816…+2pin