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}

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}

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

sin (α) = - \frac{1}{2}

cos (x) = \frac{11}{20}

sin (θ) = - \frac{1}{6}

cos (x) = 0.788

- 3 cos (x) = 2 sin^{2} (x)

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