What is the general solution for sin(x)= 5/(sqrt(29)) ?

The general solution for sin(x)= 5/(sqrt(29)) is x=1.19028…+2pin,x=pi-1.19028…+2pin

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sin(x)= 5/(sqrt(29))

sin (x) = \frac{5}{29}

x = 1.19028 \dots + 2 πn, x = π - 1.19028 \dots + 2 πn

Radians

x = 1.19028 \dots + 6.28318 \dots n, x = π - 1.19028 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{5}{29}

Simplify

\frac{5}{29} : \frac{5 29}{29}

\frac{5}{29}

Multiply by the conjugate

\frac{29}{29}

= \frac{5 29}{29 29}

2929 = 29

2929

Apply radical rule:

a a = a

2929 = 29

= 29

= \frac{5 29}{29}

sin (x) = \frac{5 29}{29}

Apply trig inverse properties

sin (x) = \frac{5 29}{29}

General solutions for

sin (x) = \frac{5 29}{29}

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

x = arcsin (\frac{5 29}{29}) + 2 πn, x = π - arcsin (\frac{5 29}{29}) + 2 πn

x = arcsin (\frac{5 29}{29}) + 2 πn, x = π - arcsin (\frac{5 29}{29}) + 2 πn

Show solutions in decimal form

x = 1.19028 \dots + 2 πn, x = π - 1.19028 \dots + 2 πn

2 sin^{2} (\frac{1}{2} x) + C = sin (x) + C

sin (a) = \frac{3}{5}, cos (a)

cos (x) = cos (4 x)

11 sin (B) + 13 = 4 sin (B) + 8

2 = 4 cos (x)

What is the general solution for sin(x)= 5/(sqrt(29)) ?
The general solution for sin(x)= 5/(sqrt(29)) is x=1.19028…+2pin,x=pi-1.19028…+2pin