What is the general solution for sin(2x-10)= 3/7 ?

The general solution for sin(2x-10)= 3/7 is x=5+pin+(0.44291…)/2 ,x=pin+pi/2-(0.44291…)/2+5

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sin(2x-10)= 3/7

Solution

sin (2 x - 10) = \frac{3}{7}

Solution

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

Degrees

x = 299.16736 \dots^{\circ} + 18 0^{\circ} n, x = 363.79043 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x - 10) = \frac{3}{7}

Apply trig inverse properties

sin (2 x - 10) = \frac{3}{7}

General solutions for

sin (2 x - 10) = \frac{3}{7}

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

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn, 2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn, 2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

Solve

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn : x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn

Move

10

to the right side

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn

Add

10

to both sides

2 x - 10 + 10 = arcsin (\frac{3}{7}) + 2 πn + 10

Simplify

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

Divide both sides by

2

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2} : 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

\frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Group like terms

= \frac{10}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{3}{7} )}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5 + \frac{2 πn}{2} + \frac{arcsin ( \frac{3}{7} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

Solve

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

Move

10

to the right side

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

Add

10

to both sides

2 x - 10 + 10 = π - arcsin (\frac{3}{7}) + 2 πn + 10

Simplify

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

Divide both sides by

2

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2} : πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

\frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

Group like terms

= \frac{π}{2} + \frac{10}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{3}{7} )}{2}

Divide the numbers:

\frac{10}{2} = 5

= \frac{π}{2} + 5 + \frac{2 πn}{2} - \frac{arcsin ( \frac{3}{7} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π}{2} + 5 + πn - \frac{arcsin ( \frac{3}{7} )}{2}

Group like terms

= πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

Show solutions in decimal form

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

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Frequently Asked Questions (FAQ)

What is the general solution for sin(2x-10)= 3/7 ?
The general solution for sin(2x-10)= 3/7 is x=5+pin+(0.44291…)/2 ,x=pin+pi/2-(0.44291…)/2+5