What is the general solution for sin(2x)=0.4 ?

The general solution for sin(2x)=0.4 is x=(0.41151…)/2+pin,x= pi/2-(0.41151…)/2+pin

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sin(2x)=0.4

sin (2 x) = 0.4

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) = 0.4

Apply trig inverse properties

sin (2 x) = 0.4

General solutions for

sin (2 x) = 0.4

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

2 x = arcsin (0.4) + 2 πn, 2 x = π - arcsin (0.4) + 2 πn

2 x = arcsin (0.4) + 2 πn, 2 x = π - arcsin (0.4) + 2 πn

Solve

2 x = arcsin (0.4) + 2 πn : x = \frac{arcsin ( 0.4 )}{2} + πn

2 x = arcsin (0.4) + 2 πn

Divide both sides by

2

2 x = arcsin (0.4) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( 0.4 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( 0.4 )}{2} + πn

x = \frac{arcsin ( 0.4 )}{2} + πn

Solve

2 x = π - arcsin (0.4) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + πn

2 x = π - arcsin (0.4) + 2 πn

Divide both sides by

2

2 x = π - arcsin (0.4) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + πn

x = \frac{arcsin ( 0.4 )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( 0.4 )}{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 (x) = - 0.4

θ, 3 cos (θ) = 1 + cos (θ)

tan (a) = \frac{5}{12}, sin (a) < 0, sin (a) + cos (a)

cot (2 x) = 3, 0 \leq x \leq 2 π

cot (θ) = \frac{5}{3}

What is the general solution for sin(2x)=0.4 ?
The general solution for sin(2x)=0.4 is x=(0.41151…)/2+pin,x= pi/2-(0.41151…)/2+pin