What is the general solution for sin(x)= 1/(sqrt(5)) ?

The general solution for sin(x)= 1/(sqrt(5)) is x=0.46364…+2pin,x=pi-0.46364…+2pin

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sin(x)= 1/(sqrt(5))

sin (x) = \frac{1}{5}

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

Radians

x = 0.46364 \dots + 6.28318 \dots n, x = π - 0.46364 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{1}{5}

Simplify

\frac{1}{5} : \frac{5}{5}

\frac{1}{5}

Multiply by the conjugate

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= \frac{5}{5}

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

cos (x) + cos (x) tan (x) = 0

4 sin^{3} (x) - sin (x) = 0

sin (θ) = 0.49

2 - sin^{2} (x) = 1 + cos (x)

2 sin^{2} (θ) - cos (θ) = 0

What is the general solution for sin(x)= 1/(sqrt(5)) ?
The general solution for sin(x)= 1/(sqrt(5)) is x=0.46364…+2pin,x=pi-0.46364…+2pin