What is the general solution for 7sin(5x)=2 ?

The general solution for 7sin(5x)=2 is x=(0.28975…)/5+(2pin)/5 ,x= pi/5-(0.28975…)/5+(2pin)/5

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7sin(5x)=2

7 sin (5 x) = 2

x = \frac{0.28975 \dots}{5} + \frac{2 πn}{5}, x = \frac{π}{5} - \frac{0.28975 \dots}{5} + \frac{2 πn}{5}

Degrees

x = 3.32030 \dots^{\circ} + 7 2^{\circ} n, x = 32.67969 \dots^{\circ} + 7 2^{\circ} n

Solution steps

7 sin (5 x) = 2

Divide both sides by

7

7 sin (5 x) = 2

Divide both sides by

7

\frac{7 sin ( 5 x )}{7} = \frac{2}{7}

Simplify

sin (5 x) = \frac{2}{7}

sin (5 x) = \frac{2}{7}

Apply trig inverse properties

sin (5 x) = \frac{2}{7}

General solutions for

sin (5 x) = \frac{2}{7}

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

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

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

Solve

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

5 x = arcsin (\frac{2}{7}) + 2 πn

Divide both sides by

5

5 x = arcsin (\frac{2}{7}) + 2 πn

Divide both sides by

5

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

Simplify

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

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

Solve

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

5 x = π - arcsin (\frac{2}{7}) + 2 πn

Divide both sides by

5

5 x = π - arcsin (\frac{2}{7}) + 2 πn

Divide both sides by

5

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.28975 \dots}{5} + \frac{2 πn}{5}, x = \frac{π}{5} - \frac{0.28975 \dots}{5} + \frac{2 πn}{5}

What is the general solution for 7sin(5x)=2 ?
The general solution for 7sin(5x)=2 is x=(0.28975…)/5+(2pin)/5 ,x= pi/5-(0.28975…)/5+(2pin)/5