What is the general solution for sin(x)= 3/(sqrt(58)) ?

The general solution for sin(x)= 3/(sqrt(58)) is x=0.40489…+2pin,x=pi-0.40489…+2pin

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sin(x)= 3/(sqrt(58))

sin (x) = \frac{3}{58}

x = 0.40489 \dots + 2 πn, x = π - 0.40489 \dots + 2 πn

Radians

x = 0.40489 \dots + 6.28318 \dots n, x = π - 0.40489 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{3}{58}

Simplify

\frac{3}{58} : \frac{3 58}{58}

\frac{3}{58}

Multiply by the conjugate

\frac{58}{58}

= \frac{3 58}{58 58}

5858 = 58

5858

Apply radical rule:

a a = a

5858 = 58

= 58

= \frac{3 58}{58}

sin (x) = \frac{3 58}{58}

Apply trig inverse properties

sin (x) = \frac{3 58}{58}

General solutions for

sin (x) = \frac{3 58}{58}

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

x = arcsin (\frac{3 58}{58}) + 2 πn, x = π - arcsin (\frac{3 58}{58}) + 2 πn

x = arcsin (\frac{3 58}{58}) + 2 πn, x = π - arcsin (\frac{3 58}{58}) + 2 πn

Show solutions in decimal form

x = 0.40489 \dots + 2 πn, x = π - 0.40489 \dots + 2 πn

cos (2 x + 1) = 0

cos (4 x) = \frac{- 3}{2}

(sec (x))^{2} = 0

3 cos (x) sin (x) = sin (x)

2 \cdot sin (x) = sin (2 x)

What is the general solution for sin(x)= 3/(sqrt(58)) ?
The general solution for sin(x)= 3/(sqrt(58)) is x=0.40489…+2pin,x=pi-0.40489…+2pin