Download Unit 5 Review Modeling Periodic Functions

Unit 5 Review Modeling Periodic Functions
Periodic Phenomena
Vocabulary: cycle, period, axis of the curve,
amplitude
Angles
Vocabulary: ray, vertex, initial arm, terminal arm, standard position, positive angle, negative angle,
quadrants of the x-y plane, coterminal angles, principal angle, related acute angle.
Trigonometric Functions - Beyond Triangles
Example:
Point P(4,-3) is on the terminal arm of an angle in standard position.
a.
Sketch the principal angle, θ.
b.
Determine the value of the related acute angle to the nearest degree.
c.
What is the measure of θ to the nearest degree?
Special Triangles
Example:
Find sin 300E without using a calculator.
The Unit Circle and Basic Sine and Cosine Graphs
Any point P(x,y) on the unit circle can be expressed as the ordered pair (cos θ, sin θ).
Transformations
Modelling Periodic Phenomena
a:
d:
The amplitude of the curve - ½ total height or distance from middle to top
The equation for the axis of the curve - split curve in half horizontally.
For sin2 it is y = 0, so the axis of a transformed curve, y = d, gives the vertical translation, d.
k:
The horizontal stretch/compression – the number of cycles that fit into one cycle of the original sin or
cos graph
k =
b:
HW:
360
new period
and
new period =
360
k
To figure out b, the phase (horizontal) shift, refer to the transformed graph:
Where have the “starting points” ended up - (0,0) for sin 2 and (0,1) for cos 2?
p 485 #1-6, 7a, 8-14, 16, 27 (with 30E instead of π/6), 30ab, 31-33
p 550 #13, 17