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Popular >

sin(5x-1)= 4/5

Solution

sin (5 x - 1) = \frac{4}{5}

Solution

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

+1

Degrees

x = 22.08517 \dots^{\circ} + 7 2^{\circ} n, x = 36.83313 \dots^{\circ} + 7 2^{\circ} n

Solution steps

sin (5 x - 1) = \frac{4}{5}

Apply trig inverse properties

sin (5 x - 1) = \frac{4}{5}

General solutions for

sin (5 x - 1) = \frac{4}{5}

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

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

Solve

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

Move

1

to the right side

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

Add

1

to both sides

5 x - 1 + 1 = arcsin (\frac{4}{5}) + 2 πn + 1

Simplify

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

Divide both sides by

5

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

Divide both sides by

5

\frac{5 x}{5} = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

Simplify

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

Solve

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

Move

1

to the right side

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

Add

1

to both sides

5 x - 1 + 1 = π - arcsin (\frac{4}{5}) + 2 πn + 1

Simplify

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

Divide both sides by

5

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

Divide both sides by

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

Simplify

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

Show solutions in decimal form

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

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