A point starts at the location (0, 4) and moves CCW along a circle centered at (0, 0). Let θ represent the number of radians the point has swept out since it started moving.
A point starts at the location (0, 4) and moves CCW along a circle centered at (0, 0). Let θ represent the number of radians the point has swept out since it started moving. Draw a diagram of this to make sure you understand the context!
a. Suppose the point has swept out 0.2 radians since it started moving (θ = 0.2). How many radians would need to be swept out from the 3- o'clock position [or from (4, 0)] to get to the point's current position?
b. Write an expression in terms of e to represent how many radians would need to be swept out from the 3-o'clock position to get to the point's current position. (Enter "theta" for 9.)
c. Write a function f that determine's the point's z-coordinate in terms 9. (Recall that 9 represents a number of radians swept out from the 12-o'clock position, not the 3-o'clock position!)
d. Sketch a graph of f.
Homework Answers
as you got function as f(theta)
= 4 sin(theta+ pi)
at theta = 0 ; f = 0
theta = pi/2 ; f = -4
theta = pi ; f = 0
theta = 3pi/2 ; f = 4
period = 2pi
amplitude = 4
phase shift = pi units to left
mid value = 0
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