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

The general solution for sin(2x)= 2/5 is x=(0.41151…)/2+pin,x= pi/2-(0.41151…)/2+pin

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sin(2x)= 2/5

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

x = \frac{0.41151 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

Degrees

x = 11.78908 \dots^{\circ} + 18 0^{\circ} n, x = 78.21091 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

2 x = arcsin (\frac{2}{5}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{2}{5}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

2 x = π - arcsin (\frac{2}{5}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{2}{5}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.41151 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

sin (2 x) + cos (x) = 0, 0 \leq x \leq 2 π

cos (θ) = - 0.5

sec (x) = \frac{5}{3}

x, y = \frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2}

3 cot^{2} (θ) - 4 csc (θ) = 1

What is the general solution for sin(2x)= 2/5 ?
The general solution for sin(2x)= 2/5 is x=(0.41151…)/2+pin,x= pi/2-(0.41151…)/2+pin