Describe each of the following properties of the graph of the Sine Function, f (theta) = sin (theta) and relate the property to the unit circle definition of sine.

Amplitude

Period

Domain

Range

x-intercepts

Hello there.

Describe each of the following properties of the graph of the Sine Function, f (theta) = sin (theta) and relate the property to the unit circle definition of sine.

x-intercepts

For the answer to the question above,

I will use t instead of theta. The question asks about f (t) = sin (t), not about some more general sine function, so I would answer as follows:

* Amplitude: 1, because largest y-coordinate of unit circle is 1

* Period: 2pi because the circumference of a unit circle is 2pi and t is measured as arc-length around the circle.

* Domain: All real numbers, because t can go as many times around the circle, both clockwise (positive) and counterclockwise (negative) as you like.

* Range: [-1, 1] because the y-coordinate on the unit circle ranges between - 1 and 1 inclusive

* x-intercepts: values of t, where y=0, namely 0 plus any integer multiple of 2pi, and pi + any integer multiple of 2pi, or, more succinctly, k pi where k is any integer.