What is the general solution for sin(2x)= 3/4 ?

The general solution for sin(2x)= 3/4 is x=(0.84806…)/2+pin,x= pi/2-(0.84806…)/2+pin

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sin(2x)= 3/4

sin (2 x) = \frac{3}{4}

x = \frac{0.84806 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.84806 \dots}{2} + πn

Solution steps

sin (2 x) = \frac{3}{4}

Apply trig inverse properties

2 x = arcsin (\frac{3}{4}) + 2 πn, 2 x = π - arcsin (\frac{3}{4}) + 2 πn

Solve

2 x = arcsin (\frac{3}{4}) + 2 πn : x = \frac{arcsin ( \frac{3}{4} )}{2} + πn

Solve

2 x = π - arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

x = \frac{arcsin ( \frac{3}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{3}{4} )}{2} + πn

Show solutions in decimal form

x = \frac{0.84806 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.84806 \dots}{2} + πn

sin (3 θ) - sin (5 θ) = sin (θ), 0 \leq θ \leq \frac{π}{2}

4 sin (2 θ) - 1 = 0

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

sec (w) csc (w) = 2 sec (w)

- 2 sin (x) - cos (2 x) \cdot 2 = 0

What is the general solution for sin(2x)= 3/4 ?
The general solution for sin(2x)= 3/4 is x=(0.84806…)/2+pin,x= pi/2-(0.84806…)/2+pin