Trigonometry

Question 1

periodic function

Answer 1

a function in which the same pattern of OUTPUTS repeat over a consistent interval in the inputs. The repeated pattern can be a wave, a zig-zag, or any other pattern that has the exact same pattern of outputs (even more complicated like a cardiac heatbeat function).

Question 2

period of a periodic function

Answer 2

the smallest interval in the domain over which a function repeats

Question 3

midline of a periodic function

Answer 3

the horizontal line located midway between the maximum and the minimum of a periodic function

Question 4

amplitude of a periodic function

Answer 4

the distance between the maximum and the midline of a periodic function

Question 5

What repeats in a periodic function?

Answer 5

It is the FUNCTION values that repeat (the outputs). To be a function, each input must have exactly one output, so there cannot be a “repeat” of any inputs.

Question 6

What does the graph look like of the height of a car/seat on a Ferris Wheel over time if the wheel is rotating at a constant speed?

Answer 6

The graph is a wave–a smoothe, curvy, periodic function. Depending on whether the bottom of the wheel is on the ground or not will determine the location of the minimum values of the wave.