What is the general solution for sin(x)= 4/(sqrt(41)) ?

The general solution for sin(x)= 4/(sqrt(41)) is x=0.67474…+2pin,x=pi-0.67474…+2pin

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sin(x)= 4/(sqrt(41))

sin (x) = \frac{4}{41}

x = 0.67474 \dots + 2 πn, x = π - 0.67474 \dots + 2 πn

Radians

x = 0.67474 \dots + 6.28318 \dots n, x = π - 0.67474 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{4}{41}

Simplify

\frac{4}{41} : \frac{4 41}{41}

\frac{4}{41}

Multiply by the conjugate

\frac{41}{41}

= \frac{4 41}{41 41}

4141 = 41

4141

Apply radical rule:

a a = a

4141 = 41

= 41

= \frac{4 41}{41}

sin (x) = \frac{4 41}{41}

Apply trig inverse properties

sin (x) = \frac{4 41}{41}

General solutions for

sin (x) = \frac{4 41}{41}

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

x = arcsin (\frac{4 41}{41}) + 2 πn, x = π - arcsin (\frac{4 41}{41}) + 2 πn

x = arcsin (\frac{4 41}{41}) + 2 πn, x = π - arcsin (\frac{4 41}{41}) + 2 πn

Show solutions in decimal form

x = 0.67474 \dots + 2 πn, x = π - 0.67474 \dots + 2 πn

2 cos (x) - sin^{2} (x) = 0

sin (x) = - 1.1

sin (x) = (\frac{3}{2})

6 sin^{2} (x) - 9 sin (x) + 3 = 0

cos (2 x) = 0.25

What is the general solution for sin(x)= 4/(sqrt(41)) ?
The general solution for sin(x)= 4/(sqrt(41)) is x=0.67474…+2pin,x=pi-0.67474…+2pin