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

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

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7sin(2x)=-2

7 sin (2 x) = - 2

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

Solution steps

7 sin (2 x) = - 2

Divide both sides by

7

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

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

sin (θ) = - \frac{( 2 )}{( 5 )}, tan (θ) > 0

(sin (x) + cos (x)) = 1

sin (θ) = 0.72437

cos (x) = \frac{5}{12}

2 cos^{2} (x) + cos (x) - 10 = 0

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