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Popular Trigonometry >

10=3.44sin(0.51t+4.11)+9.48

Solution

10 = 3.44 sin (0.51 t + 4.11) + 9.48

Solution

t = \frac{0.15174 \dots}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}, t = \frac{π}{0.51} - \frac{0.15174 \dots}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Degrees

t = - 444.68889 \dots^{\circ} + 705.88235 \dots^{\circ} n, t = - 125.84308 \dots^{\circ} + 705.88235 \dots^{\circ} n

Solution steps

10 = 3.44 sin (0.51 t + 4.11) + 9.48

Switch sides

3.44 sin (0.51 t + 4.11) + 9.48 = 10

Multiply both sides by

100

3.44 sin (0.51 t + 4.11) + 9.48 = 10

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

2

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

100

3.44 sin (0.51 t + 4.11) \cdot 100 + 9.48 \cdot 100 = 10 \cdot 100

Refine

344 sin (0.51 t + 4.11) + 948 = 1000

344 sin (0.51 t + 4.11) + 948 = 1000

Move

948

to the right side

344 sin (0.51 t + 4.11) + 948 = 1000

Subtract

948

from both sides

344 sin (0.51 t + 4.11) + 948 - 948 = 1000 - 948

Simplify

344 sin (0.51 t + 4.11) = 52

344 sin (0.51 t + 4.11) = 52

Divide both sides by

344

344 sin (0.51 t + 4.11) = 52

Divide both sides by

344

\frac{344 sin ( 0.51 t + 4.11 )}{344} = \frac{52}{344}

Simplify

sin (0.51 t + 4.11) = \frac{13}{86}

sin (0.51 t + 4.11) = \frac{13}{86}

Apply trig inverse properties

sin (0.51 t + 4.11) = \frac{13}{86}

General solutions for

sin (0.51 t + 4.11) = \frac{13}{86}

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

0.51 t + 4.11 = arcsin (\frac{13}{86}) + 2 πn, 0.51 t + 4.11 = π - arcsin (\frac{13}{86}) + 2 πn

0.51 t + 4.11 = arcsin (\frac{13}{86}) + 2 πn, 0.51 t + 4.11 = π - arcsin (\frac{13}{86}) + 2 πn

Solve

0.51 t + 4.11 = arcsin (\frac{13}{86}) + 2 πn : t = \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

0.51 t + 4.11 = arcsin (\frac{13}{86}) + 2 πn

Move

4.11

to the right side

0.51 t + 4.11 = arcsin (\frac{13}{86}) + 2 πn

Subtract

4.11

from both sides

0.51 t + 4.11 - 4.11 = arcsin (\frac{13}{86}) + 2 πn - 4.11

Simplify

0.51 t = arcsin (\frac{13}{86}) + 2 πn - 4.11

0.51 t = arcsin (\frac{13}{86}) + 2 πn - 4.11

Divide both sides by

0.51

0.51 t = arcsin (\frac{13}{86}) + 2 πn - 4.11

Divide both sides by

0.51

\frac{0.51 t}{0.51} = \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Simplify

t = \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

t = \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Solve

0.51 t + 4.11 = π - arcsin (\frac{13}{86}) + 2 πn : t = \frac{π}{0.51} - \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

0.51 t + 4.11 = π - arcsin (\frac{13}{86}) + 2 πn

Move

4.11

to the right side

0.51 t + 4.11 = π - arcsin (\frac{13}{86}) + 2 πn

Subtract

4.11

from both sides

0.51 t + 4.11 - 4.11 = π - arcsin (\frac{13}{86}) + 2 πn - 4.11

Simplify

0.51 t = π - arcsin (\frac{13}{86}) + 2 πn - 4.11

0.51 t = π - arcsin (\frac{13}{86}) + 2 πn - 4.11

Divide both sides by

0.51

0.51 t = π - arcsin (\frac{13}{86}) + 2 πn - 4.11

Divide both sides by

0.51

\frac{0.51 t}{0.51} = \frac{π}{0.51} - \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Simplify

t = \frac{π}{0.51} - \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

t = \frac{π}{0.51} - \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

t = \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}, t = \frac{π}{0.51} - \frac{arcsin ( \frac{13}{86} )}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Show solutions in decimal form

t = \frac{0.15174 \dots}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}, t = \frac{π}{0.51} - \frac{0.15174 \dots}{0.51} + \frac{2 πn}{0.51} - \frac{4.11}{0.51}

Graph

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