Download Algebra Two with Trigonometry

Introduction to Trigonometry
Notes
I.
Solve Right Triangles
A. Using the Right Triangle Definition of the Trigonometric Functions (SOH-CAH-TOA)
B. Using Special Right Triangles patterns (if solving a special right triangle)
1. 45-90-45
2.
30-60-90
C. Compare the two by using Trig. Functions on Special Right Triangles
II.
Unit Circle Terminology
A. Vocabulary
Unit Circle, angles, initial side, terminal side, standard position. positive/negative angle
measure, coterminal angles, quadrantal angles, reference angles
B. Practice worksheets
III.
Unit Circle Activity
Worksheets provided: Find and solve special right triangles on the Unit Circle to identify
some coordinates on the Unit Circle and discover the Unit Circle definition of the
trigonometric functions
IV.
Evaluate Trigonometric Functions (non-calculator)
Worksheets: Apply the Unit Circle Definition of the trigonometric functions to identify the
output value given certain input values.
V.
Solve Trigonometric Functions (calculator)
Ia-b: see handwritten worksheet
Ic. Trigonometric Functions and Special Right Triangles
Use special right triangle patterns to solve the triangles below. Then, apply the right triangle
trigonometric definitions to find the sin  , cos  , tan  (to evaluate the trig functions of each
acute angle in the triangle).
1.
2
45
Example: applying special right triangles,
I find the hypotenuse length is 2 2 units.
Then I substitute the angle measures and side lengths in the
formulas and simplify (rationalize and reduce).
opp
adj
opp
sin  
, cos 
, tan  
hyp
hyp
adj
sin 45 
2
2.
22
2
2 2

1
2
, and continue.

2
2
Find the measures of both angles, then evaluate the three trigonometric functions at each.
3.
7
7 3
14
4.
24
60
II. Unit Circle Terminology
notes
Name______________________________per_
A unit circle is a circle with a radius of ONE unit.
That unit can be any length measurement.
An Angle is formed by rotating a ray about its endpoint some number of degrees.
The number of degrees in the rotation is called the measure of the angle.
The initial side describes the ray prior to being rotated.
The terminal side describes the result of rotation.
An angle in standard position always has its initial side along the positive x-axis.
Angles with positive angle measures rotated in a counterclockwise fashion (CCW).
Angles with negative angle measures rotated in a clockwise fashion (CW).
Coterminal angles are angles with different measures, yet have overlapping
initial and terminal sides.
Quadrantal angles are angles in standard position with their terminal sides
overlapping an axis.
Reference angles are the acute angles formed between the terminal side and the
x-axis.
II. Unit Circle vocabulary practice
Name____________________________per__
Sketch the angles in standard position.
1.
45
2.
 45
3.
100
4.
180
5.
 200
6.
270
7.
360
8.
 400
9.
720
10.
1000
11.
120
12.
900
II. Unit Circle
vocabulary practice
Name__________________________per__
Name four coterminal angles for each angle given.
Be sure to include at least one negative angle measure for each.
1.
45
2.
310
3.
400
5.
 30
6.
90
7.
135
8.
330
9.
 225
10.
240
Name the reference angle for each of the given angles.
1.
45
2.
310
3.
400
5.
 30
6.
90
7.
135
8.
330
9.
 225
10.
240
Algebra Two with Trigonometry
Pre-unit circle activity worksheet
Name________________________________per___
1. Sketch the angle in standard position.
a. 120
b. 135
c. 150
d. 210
e. 225
f. 240
g. 270
h. 300
i. 315
j. 330
2. Identify the reference angle for each of the above angles.
(A reference angle is the acute angle formed between the terminal side and the x-axis.)
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
3. For each of the above angles, sketch a triangle by drawing a vertical segment from a point
on the terminal side to the x-axis. (Do this in the picture for number 1, above.)
4. For each triangle, label the hypotenuse one unit.
5. Solve each triangle. Redraw the triangles here and write in the lengths of the sides.
a. 120
b. 135
c. 150
d. 210
e. 225
f. 240
g. 270
h. 300
i. 315
j. 330
6. Use the lengths of the sides to identify the coordinates of points on the terminal side of each
angle where the terminal side intersects the unit circle. Label the coordinates on the pictures
here.
a. 120
b. 135
c. 150
d. 210
e. 225
f. 240
g. 270
h. 300
i. 315
j. 330
IV. Evaluate Trigonometric Functions
Evaluate each function without using a calculator. (Draw special right triangles in position on
the Unit Circle and apply the Unit Circle Definition of the trigonometric functions.)
1.
sin 45
2.
cos 45
3.
tan 45
4.
cos 225
5.
sin 135
6.
tan 180
7.
sin 180
8.
sin 240
9.
sin 150
10.
cos 240
11.
cos150
12.
cos180
13.
sin 330
14.
cos 315
15.
tan 300