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}

Solution steps

7 sin (5 x) = 2

Divide both sides by

7

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

Apply trig inverse properties

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}

Solve

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

arccot (x) + arccot (1 + x) = \frac{π}{4}

arcsin (x - 0.355) = 0.489

cos (\frac{π}{2} - x) = \frac{4}{5}

6 = 10 cos (4 \cdot o)

2 cos (2 θ) + 5 cos (θ) = 4

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