What is the general solution for sin(x)=(-3)/(sqrt(13)) ?

The general solution for sin(x)=(-3)/(sqrt(13)) is x=-0.98279…+2pin,x=pi+0.98279…+2pin

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sin(x)=(-3)/(sqrt(13))

sin (x) = \frac{- 3}{13}

x = - 0.98279 \dots + 2 πn, x = π + 0.98279 \dots + 2 πn

Radians

x = - 0.98279 \dots + 6.28318 \dots n, x = π + 0.98279 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{- 3}{13}

Simplify

\frac{- 3}{13} : - \frac{3 13}{13}

\frac{- 3}{13}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{13}

Rationalize

- \frac{3}{13} : - \frac{3 13}{13}

- \frac{3}{13}

Multiply by the conjugate

\frac{13}{13}

= - \frac{3 13}{13 13}

1313 = 13

1313

Apply radical rule:

a a = a

1313 = 13

= 13

= - \frac{3 13}{13}

= - \frac{3 13}{13}

sin (x) = - \frac{3 13}{13}

Apply trig inverse properties

sin (x) = - \frac{3 13}{13}

General solutions for

sin (x) = - \frac{3 13}{13}

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

x = arcsin (- \frac{3 13}{13}) + 2 πn, x = π + arcsin (\frac{3 13}{13}) + 2 πn

x = arcsin (- \frac{3 13}{13}) + 2 πn, x = π + arcsin (\frac{3 13}{13}) + 2 πn

Show solutions in decimal form

x = - 0.98279 \dots + 2 πn, x = π + 0.98279 \dots + 2 πn

3 + 2 sin (2 x) = 23

\frac{1}{1 - cos ( θ )} - \frac{1}{1 + cos ( θ )} = 2 csc^{2} (θ)

x, arctan (x + y) = y^{2} + \frac{π}{4}

- sin (x) + ln (2) \cdot cos^{2} (x) = 0

cot (x) sec (x) + 2 cot (x) = 0

What is the general solution for sin(x)=(-3)/(sqrt(13)) ?
The general solution for sin(x)=(-3)/(sqrt(13)) is x=-0.98279…+2pin,x=pi+0.98279…+2pin