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Popular >

-0.6=sin(30t)

Solution

- 0.6 = sin (30 t)

Solution

t = - \frac{0.64350 \dots}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{0.64350 \dots}{30} + \frac{πn}{15}

+1

Degrees

t = - 1.22899 \dots^{\circ} + 1 2^{\circ} n, t = 7.22899 \dots^{\circ} + 1 2^{\circ} n

Solution steps

- 0.6 = sin (30 t)

Switch sides

sin (30 t) = - 0.6

Apply trig inverse properties

sin (30 t) = - 0.6

General solutions for

sin (30 t) = - 0.6

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

30 t = arcsin (- 0.6) + 2 πn, 30 t = π + arcsin (0.6) + 2 πn

30 t = arcsin (- 0.6) + 2 πn, 30 t = π + arcsin (0.6) + 2 πn

Solve

30 t = arcsin (- 0.6) + 2 πn : t = - \frac{arcsin ( \frac{3}{5} )}{30} + \frac{πn}{15}

30 t = arcsin (- 0.6) + 2 πn

Simplify

arcsin (- 0.6) + 2 πn : - arcsin (\frac{3}{5}) + 2 πn

arcsin (- 0.6) + 2 πn

arcsin (- 0.6) = - arcsin (\frac{3}{5})

arcsin (- 0.6)

= arcsin (- \frac{3}{5})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{5}) = - arcsin (\frac{3}{5})

= - arcsin (\frac{3}{5})

= - arcsin (\frac{3}{5}) + 2 πn

30 t = - arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

30

30 t = - arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

30

\frac{30 t}{30} = - \frac{arcsin ( \frac{3}{5} )}{30} + \frac{2 πn}{30}

Simplify

t = - \frac{arcsin ( \frac{3}{5} )}{30} + \frac{πn}{15}

t = - \frac{arcsin ( \frac{3}{5} )}{30} + \frac{πn}{15}

Solve

30 t = π + arcsin (0.6) + 2 πn : t = \frac{π}{30} + \frac{arcsin ( 0.6 )}{30} + \frac{πn}{15}

30 t = π + arcsin (0.6) + 2 πn

Divide both sides by

30

30 t = π + arcsin (0.6) + 2 πn

Divide both sides by

30

\frac{30 t}{30} = \frac{π}{30} + \frac{arcsin ( 0.6 )}{30} + \frac{2 πn}{30}

Simplify

t = \frac{π}{30} + \frac{arcsin ( 0.6 )}{30} + \frac{πn}{15}

t = \frac{π}{30} + \frac{arcsin ( 0.6 )}{30} + \frac{πn}{15}

t = - \frac{arcsin ( \frac{3}{5} )}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{arcsin ( 0.6 )}{30} + \frac{πn}{15}

Show solutions in decimal form

t = - \frac{0.64350 \dots}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{0.64350 \dots}{30} + \frac{πn}{15}

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