What is the general solution for 200.4=200+sin(x/(240)) ?

The general solution for 200.4=200+sin(x/(240)) is x=240*0.41151…+480pin,x=240pi-240*0.41151…+480pin

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200.4=200+sin(x/(240))

200.4 = 200 + sin (\frac{x}{240})

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn

Degrees

x = 5658.76283 \dots^{\circ} + 86399.99999 \dots^{\circ} n, x = 37541.23716 \dots^{\circ} + 86399.99999 \dots^{\circ} n

Solution steps

200.4 = 200 + sin (\frac{x}{240})

Switch sides

200 + sin (\frac{x}{240}) = 200.4

Move

200

to the right side

200 + sin (\frac{x}{240}) = 200.4

Subtract

200

from both sides

200 + sin (\frac{x}{240}) - 200 = 200.4 - 200

Simplify

sin (\frac{x}{240}) = 0.4

sin (\frac{x}{240}) = 0.4

Apply trig inverse properties

sin (\frac{x}{240}) = 0.4

General solutions for

sin (\frac{x}{240}) = 0.4

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

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

\frac{x}{240} = arcsin (0.4) + 2 πn, \frac{x}{240} = π - arcsin (0.4) + 2 πn

Solve

\frac{x}{240} = arcsin (0.4) + 2 πn : x = 240 arcsin (0.4) + 480 πn

\frac{x}{240} = arcsin (0.4) + 2 πn

Multiply both sides by

240

\frac{x}{240} = arcsin (0.4) + 2 πn

Multiply both sides by

240

\frac{240 x}{240} = 240 arcsin (0.4) + 240 \cdot 2 πn

Simplify

x = 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn

Solve

\frac{x}{240} = π - arcsin (0.4) + 2 πn : x = 240 π - 240 arcsin (0.4) + 480 πn

\frac{x}{240} = π - arcsin (0.4) + 2 πn

Multiply both sides by

240

\frac{x}{240} = π - arcsin (0.4) + 2 πn

Multiply both sides by

240

\frac{240 x}{240} = 240 π - 240 arcsin (0.4) + 240 \cdot 2 πn

Simplify

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 π - 240 arcsin (0.4) + 480 πn

x = 240 arcsin (0.4) + 480 πn, x = 240 π - 240 arcsin (0.4) + 480 πn

Show solutions in decimal form

x = 240 \cdot 0.41151 \dots + 480 πn, x = 240 π - 240 \cdot 0.41151 \dots + 480 πn

What is the general solution for 200.4=200+sin(x/(240)) ?
The general solution for 200.4=200+sin(x/(240)) is x=240*0.41151…+480pin,x=240pi-240*0.41151…+480pin