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Popular >

0.322=sin(3.92232*t)

Solution

0.322 = sin (3.92232 \cdot t)

Solution

t = \frac{0.32784 \dots}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{0.32784 \dots}{3.92232} + \frac{2 πn}{3.92232}

+1

Degrees

t = 4.78898 \dots^{\circ} + 91.78241 \dots^{\circ} n, t = 41.10222 \dots^{\circ} + 91.78241 \dots^{\circ} n

Solution steps

0.322 = sin (3.92232 t)

Switch sides

sin (3.92232 t) = 0.322

Apply trig inverse properties

sin (3.92232 t) = 0.322

General solutions for

sin (3.92232 t) = 0.322

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

3.92232 t = arcsin (0.322) + 2 πn, 3.92232 t = π - arcsin (0.322) + 2 πn

3.92232 t = arcsin (0.322) + 2 πn, 3.92232 t = π - arcsin (0.322) + 2 πn

Solve

3.92232 t = arcsin (0.322) + 2 πn : t = \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

3.92232 t = arcsin (0.322) + 2 πn

Divide both sides by

3.92232

3.92232 t = arcsin (0.322) + 2 πn

Divide both sides by

3.92232

\frac{3.92232 t}{3.92232} = \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

Simplify

t = \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

Solve

3.92232 t = π - arcsin (0.322) + 2 πn : t = \frac{π}{3.92232} - \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

3.92232 t = π - arcsin (0.322) + 2 πn

Divide both sides by

3.92232

3.92232 t = π - arcsin (0.322) + 2 πn

Divide both sides by

3.92232

\frac{3.92232 t}{3.92232} = \frac{π}{3.92232} - \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

Simplify

t = \frac{π}{3.92232} - \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{π}{3.92232} - \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

t = \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{arcsin ( 0.322 )}{3.92232} + \frac{2 πn}{3.92232}

Show solutions in decimal form

t = \frac{0.32784 \dots}{3.92232} + \frac{2 πn}{3.92232}, t = \frac{π}{3.92232} - \frac{0.32784 \dots}{3.92232} + \frac{2 πn}{3.92232}

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