What is the general solution for sin(θ)=(sqrt(44))/(12) ?

The general solution for sin(θ)=(sqrt(44))/(12) is θ=0.58568…+2pin,θ=pi-0.58568…+2pin

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sin(θ)=(sqrt(44))/(12)

sin (θ) = \frac{44}{12}

θ = 0.58568 \dots + 2 πn, θ = π - 0.58568 \dots + 2 πn

Radians

θ = 0.58568 \dots + 6.28318 \dots n, θ = π - 0.58568 \dots + 6.28318 \dots n

Solution steps

sin (θ) = \frac{44}{12}

Simplify

\frac{44}{12} : \frac{11}{6}

\frac{44}{12}

Factor

44 : 211

Factor

44 = 2^{2} \cdot 11

= 2^{2} \cdot 11

Apply radical rule:

= 11 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 211

Factor

12 : 2^{2} \cdot 3

Factor

12 = 2^{2} \cdot 3

= \frac{2 11}{2 ^{2} \cdot 3}

Cancel the common factor:

2

= \frac{11}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{11}{6}

Apply trig inverse properties

sin (θ) = \frac{11}{6}

General solutions for

sin (θ) = \frac{11}{6}

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

θ = arcsin (\frac{11}{6}) + 2 πn, θ = π - arcsin (\frac{11}{6}) + 2 πn

θ = arcsin (\frac{11}{6}) + 2 πn, θ = π - arcsin (\frac{11}{6}) + 2 πn

Show solutions in decimal form

θ = 0.58568 \dots + 2 πn, θ = π - 0.58568 \dots + 2 πn

cos (A) = \frac{2 ^{2} + 2.2 4 ^{2} - 2.2 4 ^{2}}{2 ( 2 ) ( 2.24 )}

cos (θ) = - \frac{3}{5}, θ, 3

sin (3 x) = 0.5

cos^{2} (x) - 5 sin (x) + 5 = 0

- 4 + cos (4 θ) = \frac{- 8 + 3}{2}

What is the general solution for sin(θ)=(sqrt(44))/(12) ?
The general solution for sin(θ)=(sqrt(44))/(12) is θ=0.58568…+2pin,θ=pi-0.58568…+2pin