Download Unit 9 doc - New Paltz Central School District

Reflective Portfolio
Unit #9: Trigonometry
Section #1: Vocabulary (words and/or diagrams)
Define each: Use words or a LABELED diagram.
Acute angle
Angle in standard
position
Initial side
Terminal side
Co-terminal angle
Reference angle
Periodic function
Quadrantal angle
Reference Triangle
Radian
Sinusoidal graphs
Amplitude
period
frequency
midline
vertical shift
Section #2: Formulas/Equations/Rules

Draw and label the Special Right Triangle Ratios (45-45-90, 30-60-90)

State the Pythagorean TRIG identity:


Number the quadrants
Label the signs of an ordered pair in each quadrant

State the 3 basic trig functions and their corresponding Reciprocal Functions
Basic trig functions


Reciprocal trig functions
In the unit circle, the cosine is the ____-coordinate, the sine is the _____-coordinate and the
tangent is what quotient in terms of cos and sin?
s  r
where
s represent the __________ _____________, 
___________ in ______________, and
r
represents the _____________
represents the ___________________.
1) How long (in terms of pi) is the arc subtended by an angle of
cm?
radians on a circle of radius 40
2) A central angle of a circular garden measures 120 degrees and intercepts an arc of 90 feet. What is
the radius of the garden measured to the nearest foot?
Section #3: Key methods and concepts
 Find a positive and negative co-terminal angle for each:
a) 135º

b) 330º
c)

4
c)

4
Find the ordered pair that lies on the unit circle for each angle:
Draw the reference triangle for each!!!!
a) 135º

b) 330º
How to find the exact value of a trigonometric function
o Include the following examples: (notice the work is done above.)
a) cos 135º
b) csc 330º
c) tan

4

How to convert radians to degrees
o Include this example: Convert
5
to degrees
3

How to convert degrees to radians
o Include this example: Convert 315o to radians

If sin   
3
and 270    360 , find the exact value of the other 5 trigonometric functions.
5
 Trig Graphs to know
y=sin(x)
y=cos(x)
What is the difference between the graph of the sine function and the graph of the cosine function?

Graph the following:
y= -2cos(x)+1
amplitude=_____ frequency=____ period=______
vertical shift:_____ midline=________

Trig Graphs: Apply to real-life
1)
(trig equation)
a sine graph with the following parameters
amplitude=__2__ period=___π___ midline: y  1