Download Trigonometry - Baltimore City Public Schools

ALGEBRA II WITH TRIGONOMETRY
MR. YATES
UNIT 4: TRIGONOMETRY
UNIT OUTLINE.
I.
Vocabulary
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Right Triangle
Pythagorean Theorem
Sine
Cosine
Tangent
Ratio
Trig Inverses
Law of Sines
Law of Cosines
Unit Circle
Radius
Angle
Standard Position
Initial Side
Terminal Side
Degrees
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Radians
Cartesian Coordinates (x,y)
Slope
Periodic Function
Cycle
Domain
Range
Maximum
Minimum
Amplitude
Period
Zeros
Sine Function
Cosine Function
Tangent Function
Asymptote
II.
Trig of the Right Triangle
A. Know the definitions of sine, cosine, and tangent (SOHCAHTOA)
B. Find the sine, cosine, or tangent of a given angle, using their
definitions and a picture
C. Find the sine, cosine, or tangent of a given angle, using a
calculator or a trig table
D. Set up a proportion to solve for a missing side
E. Use inverses to find a missing angle
F. Use the Pythagorean Theorem c 2  a 2  b 2
G. Draw a diagram to represent a real-world situation
III.
Trig of Other Triangles
sin A sin B sin C
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a
b
c
2
2
2
B. Law of Cosines: c  a  b  2ab cosC 
C. Use the Law of Sines if you have two angles and a side opposite
one of them
A. Law of Sines:
D. Use the Law of Sines if you have two sides and an angle opposite
one of them
E. Use the Law of Cosines if you have all sides and wish to know an
angle (opposite side c)
F. Use the Law of Cosines if your have two sides and the angle
opposite the side you wish to know
IV.
Trig of the Unit Circle
A. Measure angles in degrees
B. Convert between degrees and radians (conversion factor is /180
or 180/)
C. Draw an angle in standard position
D. Find the coordinates of the point where the terminal side meets
the unit circle
 x = cos 
 y = sin 
E. Find the slope of the terminal side (tan )
F. Use the unit circle to help you with solving trig equations
V.
Periodic Functions
A. Sketch the graph of a periodic function
B. Identify the domain (possible x-values) and range (possible yvalues) of a function
C. Identify the zeros, maxima, and minima of a function
D. Identify the period (length, in the x-direction, of one cycle)
E. Identify the amplitude (half the total height, in the y-direction)
F. Use the equation of a sine, cosine or tangent function transformed
to determine period and amplitude
a. y = a sin (b): |a| = amplitude, 2/b = period
b. y = a cos (b): |a| = amplitude, 2/b = period
c. y = a tan (b): amplitude is infinite, /b = period
VI.
Solving Trig Equations
A. Solve by doing the opposite of each operation
B. Use the unit circle to identify multiple angles that have the same
sine, cosine, or tangent, to find multiple solutions
C. Solve by graphing the function and the value it’s supposed to
equal on the calculator, and finding points of intersection
Homework Assignment
Date __________________ Name ________________________
5… 4… 3… 2… 1
You may review your notes, the unit outline, and/or your book, to help you below.
5 Skills You Have Learned
List them by skill name or example
4 Vocab Words You Know
Define them in your own words without looking in a glossary
3 Examples of Questions You Can Do
Write three algebraic challenges (can be taken from classwork) along with worked-out solutions, showing all work
2 Skills You Still Struggle With
List them by skill name or example
1 Vocab Word You Are Unfamiliar With
Just list the word