What is the general solution for sin(2x)= 4/5 ?

The general solution for sin(2x)= 4/5 is x=(0.92729…)/2+pin,x= pi/2-(0.92729…)/2+pin

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sin(2x)= 4/5

sin (2 x) = \frac{4}{5}

x = \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

Degrees

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n, x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = \frac{4}{5}

Apply trig inverse properties

sin (2 x) = \frac{4}{5}

General solutions for

sin (2 x) = \frac{4}{5}

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

2 x = arcsin (\frac{4}{5}) + 2 πn, 2 x = π - arcsin (\frac{4}{5}) + 2 πn

2 x = arcsin (\frac{4}{5}) + 2 πn, 2 x = π - arcsin (\frac{4}{5}) + 2 πn

Solve

2 x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{2} + πn

2 x = arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{4}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = \frac{arcsin ( \frac{4}{5} )}{2} + πn

Solve

2 x = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{4}{5} )}{2} + πn

2 x = π - arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{4}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{4}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = \frac{arcsin ( \frac{4}{5} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{4}{5} )}{2} + πn

Show solutions in decimal form

x = \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

2 csc (x) + 17 = 15 + csc (x)

cos (x) - sin (x) = 2

cot (θ) = (5.8473)

6 = 2 + 5 arctan (\frac{x}{2})

tan^{2} (θ) - 2 sec (θ) = 2

What is the general solution for sin(2x)= 4/5 ?
The general solution for sin(2x)= 4/5 is x=(0.92729…)/2+pin,x= pi/2-(0.92729…)/2+pin