What is the general solution for sin(θ)= 3/(3sqrt(5)) ?

The general solution for sin(θ)= 3/(3sqrt(5)) is θ=0.46364…+2pin,θ=pi-0.46364…+2pin

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sin(θ)= 3/(3sqrt(5))

sin (θ) = \frac{3}{3 5}

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

Radians

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

Solution steps

sin (θ) = \frac{3}{3 5}

Simplify

\frac{3}{3 5} : \frac{5}{5}

\frac{3}{3 5}

Divide the numbers:

\frac{3}{3} = 1

= \frac{1}{5}

Rationalize

\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}

= \frac{5}{5}

sin (θ) = \frac{5}{5}

Apply trig inverse properties

sin (θ) = \frac{5}{5}

General solutions for

sin (θ) = \frac{5}{5}

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

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

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

Show solutions in decimal form

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

6 cos (θ) sin (θ) + cos (θ) = 0

cos (x) + cos (5 x) = 0

7 cos (t) + 5 sin (t) = 0

cos (X) = 0.4848

\frac{π}{3} = 3 + 2 sin (2 t)

What is the general solution for sin(θ)= 3/(3sqrt(5)) ?
The general solution for sin(θ)= 3/(3sqrt(5)) is θ=0.46364…+2pin,θ=pi-0.46364…+2pin