What is the general solution for sin(2x)=-2/13 ?

The general solution for sin(2x)=-2/13 is x=-(0.15445…)/2+pin,x= pi/2+(0.15445…)/2+pin

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sin(2x)=-2/13

sin (2 x) = - \frac{2}{13}

x = - \frac{0.15445 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.15445 \dots}{2} + πn

Solution steps

sin (2 x) = - \frac{2}{13}

Apply trig inverse properties

2 x = arcsin (- \frac{2}{13}) + 2 πn, 2 x = π + arcsin (\frac{2}{13}) + 2 πn

Solve

2 x = arcsin (- \frac{2}{13}) + 2 πn : x = - \frac{arcsin ( \frac{2}{13} )}{2} + πn

Solve

2 x = π + arcsin (\frac{2}{13}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{2}{13} )}{2} + πn

x = - \frac{arcsin ( \frac{2}{13} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2}{13} )}{2} + πn

Show solutions in decimal form

x = - \frac{0.15445 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.15445 \dots}{2} + πn

tan (x) - 2 = 3, 0^{\circ} \leq x \leq 36 0^{\circ}

1 = 4 - 6 sin (x)

tan (θ) + 1 = 0, 0 \leq θ \leq 2 π

2 - sin (2 θ) = 4 sin (2 θ)

2 sin (θ) cos (θ) + sin (θ) = 0

What is the general solution for sin(2x)=-2/13 ?
The general solution for sin(2x)=-2/13 is x=-(0.15445…)/2+pin,x= pi/2+(0.15445…)/2+pin