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

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

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sin(x)=sqrt(3/4)

sin (x) = \frac{3}{4}

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

Solution steps

sin (x) = \frac{3}{4}

Simplify

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

\frac{3}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3}{2}

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

General solutions for

sin (x) = \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}

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

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

2 sin (2 x) = 3 sin (x)

4 sin (\frac{t}{2}) - 1 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

- 6 cos (θ) - 10 = - 7

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

tanh (x) = 1

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