What is the general solution for -0.002=sin(2pi*(3)-500pi(0)+x) ?

The general solution for -0.002=sin(2pi*(3)-500pi(0)+x) is x=-0.00200…+2pin-6pi,x=-5pi+2pin+0.00200…

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Popular Trigonometry >

-0.002=sin(2pi*(3)-500pi(0)+x)

Solution

- 0.002 = sin (2 π \cdot (3) - 500 π (0) + x)

Solution

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

Degrees

x = - 1080.11459 \dots^{\circ} + 36 0^{\circ} n, x = - 899.88540 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 0.002 = sin (2 π (3) - 500 π (0) + x)

Switch sides

sin (2 π 3 - 500 π 0 + x) = - 0.002

Apply trig inverse properties

sin (2 π 3 - 500 π 0 + x) = - 0.002

General solutions for

sin (2 π 3 - 500 π 0 + x) = - 0.002

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

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

Solve

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn : x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn

Simplify

2 π 3 - 500 π 0 + x : x + 6 π

2 π 3 - 500 π 0 + x

Multiply the numbers:

2 \cdot 3 = 6

= 6 π - 500 \cdot 0 π + x

Apply rule

0 \cdot a = 0

= 6 π - 0 + x

6 π - 0 + x = 6 π + x

= x + 6 π

Simplify

arcsin (- 0.002) + 2 πn : - arcsin (\frac{1}{500}) + 2 πn

arcsin (- 0.002) + 2 πn

arcsin (- 0.002) = - arcsin (\frac{1}{500})

arcsin (- 0.002)

= arcsin (- \frac{1}{500})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{500}) = - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500})

= - arcsin (\frac{1}{500}) + 2 πn

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

Move

6 π

to the right side

x + 6 π = - arcsin (\frac{1}{500}) + 2 πn

Subtract

6 π

from both sides

x + 6 π - 6 π = - arcsin (\frac{1}{500}) + 2 πn - 6 π

Simplify

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

Solve

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn : x = - 5 π + 2 πn + arcsin (0.002)

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

Multiply the numbers:

2 \cdot 3 = 6

6 π - 500 \cdot 0 π + x = π + arcsin (0.002) + 2 πn

Apply rule

0 \cdot a = 0

6 π - 0 + x = π + arcsin (0.002) + 2 πn

6 π - 0 + x = 6 π + x

x + 6 π = π + arcsin (0.002) + 2 πn

Move

6 π

to the right side

x + 6 π = π + arcsin (0.002) + 2 πn

Subtract

6 π

from both sides

x + 6 π - 6 π = π + arcsin (0.002) + 2 πn - 6 π

Simplify

x = - 5 π + 2 πn + arcsin (0.002)

x = - 5 π + 2 πn + arcsin (0.002)

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π, x = - 5 π + 2 πn + arcsin (0.002)

Show solutions in decimal form

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -0.002=sin(2pi*(3)-500pi(0)+x) ?
The general solution for -0.002=sin(2pi*(3)-500pi(0)+x) is x=-0.00200…+2pin-6pi,x=-5pi+2pin+0.00200…