how do you find all the values of theta from 0 degrees through 360 degrees for which sin theta equals 0

In google type:

Graphs of the trigonometric functions

You will find many sites with graph of

y=sin(x)

or

y=sin(theta)

sin(theta)=0 for:

theta=0

theta= pi radians or theta=180°

and

theta= 2pi radians or theta=360°

(20 degree, 210 degree)

To find all the values of theta from 0 degrees through 360 degrees for which sin theta equals 0, follow these steps:

1. Recall that the sine function, sin(theta), equals 0 when theta is equal to multiples of 180 degrees.
2. Start with theta = 0 degrees, and increment theta by 180 degrees until reaching 360 degrees.
3. Record all values of theta where sin theta equals 0.
4. The values of theta that satisfy sin theta equals 0 are: 0 degrees, 180 degrees, and 360 degrees.

To find all the values of θ from 0 degrees through 360 degrees for which sin θ equals 0, we need to solve the equation sin θ = 0.

The property of sin θ being equal to 0 means that the sine function has a value of 0 at those specific angles. The sine function is equal to 0 at angles where the terminal side of the angle intersects with the x-axis on the unit circle.

To solve the equation sin θ = 0, we can utilize the fact that the sine function is equal to 0 at specific angles. These angles are 0 degrees, 180 degrees, and any other angle that is a multiple of 360 degrees (or 2π radians). This is because the sine function has a repeating pattern with a period of 360 degrees or 2π radians.

So, the values of θ from 0 degrees through 360 degrees (including 0 and 360 degrees) for which sin θ equals 0 are:
- 0 degrees
- 180 degrees
- Any angle θ that satisfies the equation θ = 360n, where n is an integer.

In summary, to find all the values of θ from 0 degrees through 360 degrees for which sin θ equals 0, we consider the angles where the sine function is equal to 0, which are 0 degrees, 180 degrees, and any angle that is a multiple of 360 degrees.