What is the general solution for sin(θ)=sqrt(3/4) ?

The general solution for sin(θ)=sqrt(3/4) is θ= pi/3+2pin,θ=(2pi)/3+2pin

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sin(θ)=sqrt(3/4)

sin (θ) = \frac{3}{4}

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

Solution steps

sin (θ) = \frac{3}{4}

Simplify

\frac{3}{4} : \frac{3}{2}

\frac{3}{4}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

sin (θ) = \frac{3}{2}

General solutions for

sin (θ) = \frac{3}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

3 cos (t) = 0

cos (θ) = \frac{7}{9}

1 - cot^{2} (x) = 0

cot^{2} (x) - 2 csc^{2} (x) + 5 = 0

3 tan (x) = 3, 0 \leq x < 2 π

What is the general solution for sin(θ)=sqrt(3/4) ?
The general solution for sin(θ)=sqrt(3/4) is θ= pi/3+2pin,θ=(2pi)/3+2pin