What is the general solution for sin(x-pi/3)=0.4 ?

The general solution for sin(x-pi/3)=0.4 is x=0.41151…+2pin+pi/3 ,x=pi-0.41151…+2pin+pi/3

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sin(x-pi/3)=0.4

sin (x - \frac{π}{3}) = 0.4

x = 0.41151 \dots + 2 πn + \frac{π}{3}, x = π - 0.41151 \dots + 2 πn + \frac{π}{3}

Degrees

x = 83.57817 \dots^{\circ} + 36 0^{\circ} n, x = 216.42182 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x - \frac{π}{3}) = 0.4

Apply trig inverse properties

sin (x - \frac{π}{3}) = 0.4

General solutions for

sin (x - \frac{π}{3}) = 0.4

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

x - \frac{π}{3} = arcsin (0.4) + 2 πn, x - \frac{π}{3} = π - arcsin (0.4) + 2 πn

x - \frac{π}{3} = arcsin (0.4) + 2 πn, x - \frac{π}{3} = π - arcsin (0.4) + 2 πn

Solve

x - \frac{π}{3} = arcsin (0.4) + 2 πn : x = arcsin (0.4) + 2 πn + \frac{π}{3}

x - \frac{π}{3} = arcsin (0.4) + 2 πn

Move

\frac{π}{3}

to the right side

x - \frac{π}{3} = arcsin (0.4) + 2 πn

Add

\frac{π}{3}

to both sides

x - \frac{π}{3} + \frac{π}{3} = arcsin (0.4) + 2 πn + \frac{π}{3}

Simplify

x = arcsin (0.4) + 2 πn + \frac{π}{3}

x = arcsin (0.4) + 2 πn + \frac{π}{3}

Solve

x - \frac{π}{3} = π - arcsin (0.4) + 2 πn : x = π - arcsin (0.4) + 2 πn + \frac{π}{3}

x - \frac{π}{3} = π - arcsin (0.4) + 2 πn

Move

\frac{π}{3}

to the right side

x - \frac{π}{3} = π - arcsin (0.4) + 2 πn

Add

\frac{π}{3}

to both sides

x - \frac{π}{3} + \frac{π}{3} = π - arcsin (0.4) + 2 πn + \frac{π}{3}

Simplify

x = π - arcsin (0.4) + 2 πn + \frac{π}{3}

x = π - arcsin (0.4) + 2 πn + \frac{π}{3}

x = arcsin (0.4) + 2 πn + \frac{π}{3}, x = π - arcsin (0.4) + 2 πn + \frac{π}{3}

Show solutions in decimal form

x = 0.41151 \dots + 2 πn + \frac{π}{3}, x = π - 0.41151 \dots + 2 πn + \frac{π}{3}

2 sin^{2} (θ) - 2 = cos^{2} (θ)

sin (θ) + cos (θ) = \frac{3}{2}

2 cos^{2} (a) = cos (a)

\frac{1}{2} = cos (2 θ)

(tan (x) - 1) (2 sin (x) + 1) = 0

What is the general solution for sin(x-pi/3)=0.4 ?
The general solution for sin(x-pi/3)=0.4 is x=0.41151…+2pin+pi/3 ,x=pi-0.41151…+2pin+pi/3