What is the general solution for 8/17 =sin(2x) ?

The general solution for 8/17 =sin(2x) is x=(0.48995…)/2+pin,x= pi/2-(0.48995…)/2+pin

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8/17 =sin(2x)

\frac{8}{17} = sin (2 x)

x = \frac{0.48995 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.48995 \dots}{2} + πn

Solution steps

\frac{8}{17} = sin (2 x)

Switch sides

sin (2 x) = \frac{8}{17}

Apply trig inverse properties

2 x = arcsin (\frac{8}{17}) + 2 πn, 2 x = π - arcsin (\frac{8}{17}) + 2 πn

Solve

2 x = arcsin (\frac{8}{17}) + 2 πn : x = \frac{arcsin ( \frac{8}{17} )}{2} + πn

Solve

2 x = π - arcsin (\frac{8}{17}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

x = \frac{arcsin ( \frac{8}{17} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

Show solutions in decimal form

x = \frac{0.48995 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.48995 \dots}{2} + πn

sec (2 x) + tan (2 x) = 2

sec (2 x) + tan (2 x) = 9

2 + 3 cos^{2} (x) = sin^{2} (x) + 4 cos (x)

sin (x) - 3 cos (x) = 0

tan (4 x) - tan (2 x) = 0

What is the general solution for 8/17 =sin(2x) ?
The general solution for 8/17 =sin(2x) is x=(0.48995…)/2+pin,x= pi/2-(0.48995…)/2+pin