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Popular Trigonometry >

sin(6.5x+2.5)=0.0851

Solution

sin (6.5 x + 2.5) = 0.0851

Solution

x = \frac{0.08520 \dots}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}, x = \frac{π}{6.5} - \frac{0.08520 \dots}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

+1

Degrees

x = - 21.28579 \dots^{\circ} + 55.38461 \dots^{\circ} n, x = 4.90442 \dots^{\circ} + 55.38461 \dots^{\circ} n

Solution steps

sin (6.5 x + 2.5) = 0.0851

Apply trig inverse properties

sin (6.5 x + 2.5) = 0.0851

General solutions for

sin (6.5 x + 2.5) = 0.0851

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

6.5 x + 2.5 = arcsin (0.0851) + 2 πn, 6.5 x + 2.5 = π - arcsin (0.0851) + 2 πn

6.5 x + 2.5 = arcsin (0.0851) + 2 πn, 6.5 x + 2.5 = π - arcsin (0.0851) + 2 πn

Solve

6.5 x + 2.5 = arcsin (0.0851) + 2 πn : x = \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

6.5 x + 2.5 = arcsin (0.0851) + 2 πn

Move

2.5

to the right side

6.5 x + 2.5 = arcsin (0.0851) + 2 πn

Subtract

2.5

from both sides

6.5 x + 2.5 - 2.5 = arcsin (0.0851) + 2 πn - 2.5

Simplify

6.5 x = arcsin (0.0851) + 2 πn - 2.5

6.5 x = arcsin (0.0851) + 2 πn - 2.5

Divide both sides by

6.5

6.5 x = arcsin (0.0851) + 2 πn - 2.5

Divide both sides by

6.5

\frac{6.5 x}{6.5} = \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

Simplify

x = \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

x = \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

Solve

6.5 x + 2.5 = π - arcsin (0.0851) + 2 πn : x = \frac{π}{6.5} - \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

6.5 x + 2.5 = π - arcsin (0.0851) + 2 πn

Move

2.5

to the right side

6.5 x + 2.5 = π - arcsin (0.0851) + 2 πn

Subtract

2.5

from both sides

6.5 x + 2.5 - 2.5 = π - arcsin (0.0851) + 2 πn - 2.5

Simplify

6.5 x = π - arcsin (0.0851) + 2 πn - 2.5

6.5 x = π - arcsin (0.0851) + 2 πn - 2.5

Divide both sides by

6.5

6.5 x = π - arcsin (0.0851) + 2 πn - 2.5

Divide both sides by

6.5

\frac{6.5 x}{6.5} = \frac{π}{6.5} - \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

Simplify

x = \frac{π}{6.5} - \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

x = \frac{π}{6.5} - \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

x = \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}, x = \frac{π}{6.5} - \frac{arcsin ( 0.0851 )}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

Show solutions in decimal form

x = \frac{0.08520 \dots}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}, x = \frac{π}{6.5} - \frac{0.08520 \dots}{6.5} + \frac{2 πn}{6.5} - \frac{2.5}{6.5}

Graph

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