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Popular Trigonometry >

5.8=11.8sin(3.78*t)

Solution

5.8 = 11.8 sin (3.78 \cdot t)

Solution

t = \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}

Degrees

t = 7.78859 \dots^{\circ} + 95.23809 \dots^{\circ} n, t = 39.83045 \dots^{\circ} + 95.23809 \dots^{\circ} n

Solution steps

5.8 = 11.8 sin (3.78 t)

Switch sides

11.8 sin (3.78 t) = 5.8

Multiply both sides by

10

11.8 sin (3.78 t) = 5.8

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

11.8 sin (3.78 t) \cdot 10 = 5.8 \cdot 10

Refine

118 sin (3.78 t) = 58

118 sin (3.78 t) = 58

Divide both sides by

118

118 sin (3.78 t) = 58

Divide both sides by

118

\frac{118 sin ( 3.78 t )}{118} = \frac{58}{118}

Simplify

sin (3.78 t) = \frac{29}{59}

sin (3.78 t) = \frac{29}{59}

Apply trig inverse properties

sin (3.78 t) = \frac{29}{59}

General solutions for

sin (3.78 t) = \frac{29}{59}

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

3.78 t = arcsin (\frac{29}{59}) + 2 πn, 3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

3.78 t = arcsin (\frac{29}{59}) + 2 πn, 3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

Solve

3.78 t = arcsin (\frac{29}{59}) + 2 πn : t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

3.78 t = arcsin (\frac{29}{59}) + 2 πn

Divide both sides by

3.78

3.78 t = arcsin (\frac{29}{59}) + 2 πn

Divide both sides by

3.78

\frac{3.78 t}{3.78} = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

Simplify

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

Solve

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn : t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

Divide both sides by

3.78

3.78 t = π - arcsin (\frac{29}{59}) + 2 πn

Divide both sides by

3.78

\frac{3.78 t}{3.78} = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

Simplify

t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

t = \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{arcsin ( \frac{29}{59} )}{3.78} + \frac{2 πn}{3.78}

Show solutions in decimal form

t = \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}, t = \frac{π}{3.78} - \frac{0.51384 \dots}{3.78} + \frac{2 πn}{3.78}

Graph

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