What is the general solution for sin(a)=-5/13 ?

The general solution for sin(a)=-5/13 is a=-0.39479…+2pin,a=pi+0.39479…+2pin

sin(a)=-5/13

sin (a) = - \frac{5}{13}

a = - 0.39479 \dots + 2 πn, a = π + 0.39479 \dots + 2 πn

Degrees

a = - 22.61986 \dots^{\circ} + 36 0^{\circ} n, a = 202.61986 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = - \frac{5}{13}

Apply trig inverse properties

sin (a) = - \frac{5}{13}

General solutions for

sin (a) = - \frac{5}{13}

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

a = arcsin (- \frac{5}{13}) + 2 πn, a = π + arcsin (\frac{5}{13}) + 2 πn

a = arcsin (- \frac{5}{13}) + 2 πn, a = π + arcsin (\frac{5}{13}) + 2 πn

Show solutions in decimal form

a = - 0.39479 \dots + 2 πn, a = π + 0.39479 \dots + 2 πn

sin (x) = \frac{13}{14}

sin (x - \frac{π}{2}) + sin (\frac{π}{2}) = sin (x + \frac{π}{2})

cos (y) = 0.8192

x, 1.56 sin (2 x) = 2 \cdot sin (x) cos (x)

\frac{7}{sin ( 7 0 ^{\circ} )} = \frac{5}{sin ( b )}

What is the general solution for sin(a)=-5/13 ?
The general solution for sin(a)=-5/13 is a=-0.39479…+2pin,a=pi+0.39479…+2pin