What is the general solution for sin(x)=-8/(8sqrt(13)) ?

The general solution for sin(x)=-8/(8sqrt(13)) is x=-0.28103…+2pin,x=pi+0.28103…+2pin

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sin(x)=-8/(8sqrt(13))

sin (x) = - \frac{8}{8 13}

x = - 0.28103 \dots + 2 πn, x = π + 0.28103 \dots + 2 πn

Radians

x = - 0.28103 \dots + 6.28318 \dots n, x = π + 0.28103 \dots + 6.28318 \dots n

Solution steps

sin (x) = - \frac{8}{8 13}

Simplify

- \frac{8}{8 13} : - \frac{13}{13}

- \frac{8}{8 13}

Divide the numbers:

\frac{8}{8} = 1

= - \frac{1}{13}

Rationalize

- \frac{1}{13} : - \frac{13}{13}

- \frac{1}{13}

Multiply by the conjugate

\frac{13}{13}

= - \frac{1 \cdot 13}{13 13}

1 \cdot 13 = 13

1313 = 13

1313

Apply radical rule:

a a = a

1313 = 13

= 13

= - \frac{13}{13}

= - \frac{13}{13}

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = - 0.28103 \dots + 2 πn, x = π + 0.28103 \dots + 2 πn

cos (x) = 1.76819

2 sin (2 x) = sin (2 x)

- 3 sin (2 x) = cos (2 x)

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

cos (2 θ) = (\frac{57}{11})

What is the general solution for sin(x)=-8/(8sqrt(13)) ?
The general solution for sin(x)=-8/(8sqrt(13)) is x=-0.28103…+2pin,x=pi+0.28103…+2pin