5sin(62.83x)=-0.32

Solution

5 sin (62.83 x) = - 0.32

x = - \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}

Solution steps

5 sin (62.83 x) = - 0.32

Divide both sides by

5

sin (62.83 x) = - 0.064

Apply trig inverse properties

62.83 x = arcsin (- 0.064) + 2 πn, 62.83 x = π + arcsin (0.064) + 2 πn

Solve

62.83 x = arcsin (- 0.064) + 2 πn : x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}

Solve

62.83 x = π + arcsin (0.064) + 2 πn : x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

Show solutions in decimal form

x = - \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}

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