What is the general solution for sin(2x)= 3/5 ?

The general solution for sin(2x)= 3/5 is x=(0.64350…)/2+pin,x= pi/2-(0.64350…)/2+pin

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sin(2x)= 3/5

sin (2 x) = \frac{3}{5}

x = \frac{0.64350 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.64350 \dots}{2} + πn

Degrees

x = 18.43494 \dots^{\circ} + 18 0^{\circ} n, x = 71.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = \frac{3}{5}

Apply trig inverse properties

sin (2 x) = \frac{3}{5}

General solutions for

sin (2 x) = \frac{3}{5}

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

2 x = arcsin (\frac{3}{5}) + 2 πn, 2 x = π - arcsin (\frac{3}{5}) + 2 πn

2 x = arcsin (\frac{3}{5}) + 2 πn, 2 x = π - arcsin (\frac{3}{5}) + 2 πn

Solve

2 x = arcsin (\frac{3}{5}) + 2 πn : x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

2 x = arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

Solve

2 x = π - arcsin (\frac{3}{5}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

2 x = π - arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

Show solutions in decimal form

x = \frac{0.64350 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.64350 \dots}{2} + πn

- cos (x) = sin (x)

2 cos^{2} (x) + 5 cos (x) - 3 = 0

x, cos (x) = 1

cos (x) cot^{2} (x) = cos (x)

4 sin (x) cos (x) = - 9 cos (x)

What is the general solution for sin(2x)= 3/5 ?
The general solution for sin(2x)= 3/5 is x=(0.64350…)/2+pin,x= pi/2-(0.64350…)/2+pin