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Popular Trigonometry >

6.15=220sin(377t)

Solution

6.15 = 220 sin (377 t)

Solution

t = \frac{0.02795 \dots}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{0.02795 \dots}{377} + \frac{2 πn}{377}

+1

Degrees

t = 0.00424 \dots^{\circ} + 0.95490 \dots^{\circ} n, t = 0.47320 \dots^{\circ} + 0.95490 \dots^{\circ} n

Solution steps

6.15 = 220 sin (377 t)

Switch sides

220 sin (377 t) = 6.15

Divide both sides by

220

220 sin (377 t) = 6.15

Divide both sides by

220

\frac{220 sin ( 377 t )}{220} = \frac{6.15}{220}

Simplify

sin (377 t) = 0.02795 \dots

sin (377 t) = 0.02795 \dots

Apply trig inverse properties

sin (377 t) = 0.02795 \dots

General solutions for

sin (377 t) = 0.02795 \dots

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

377 t = arcsin (0.02795 \dots) + 2 πn, 377 t = π - arcsin (0.02795 \dots) + 2 πn

377 t = arcsin (0.02795 \dots) + 2 πn, 377 t = π - arcsin (0.02795 \dots) + 2 πn

Solve

377 t = arcsin (0.02795 \dots) + 2 πn : t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

377 t = arcsin (0.02795 \dots) + 2 πn

Divide both sides by

377

377 t = arcsin (0.02795 \dots) + 2 πn

Divide both sides by

377

\frac{377 t}{377} = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Simplify

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Solve

377 t = π - arcsin (0.02795 \dots) + 2 πn : t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

377 t = π - arcsin (0.02795 \dots) + 2 πn

Divide both sides by

377

377 t = π - arcsin (0.02795 \dots) + 2 πn

Divide both sides by

377

\frac{377 t}{377} = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Simplify

t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Show solutions in decimal form

t = \frac{0.02795 \dots}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{0.02795 \dots}{377} + \frac{2 πn}{377}

Graph

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