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Notes 4.2 – Unit Circle
Pre-Calc. for AP Prep.
Date: ______
Goal: To use reference angles and quadrants to develop a feel for trigonometric functions
of special and general angles. to connect special right triangles to the unit circle.
Before we start evaluating trig. functions without a calculator, we need to recall a few
important facts.

Identify which trig. functions are positive in which quadrants.

All six trig. functions in terms of sides of a right triangle:

sin  
csc  
cos  
sec  
tan  
cot  
30°-60°-90° Triangles

45°-45°-90° Triangles
I. Evaluating trigonometric functions without a calculator.
 Angles with major angles as reference angles.
1. Determine the position (reference angle and quadrant) of the terminal
side.
2. Consider the definition of the trigonometric function to find
the value of the function.
3. Consider the quadrant when determining whether a trigonometric
function is positive or negative.

For quadrantal angles we need to remember the following:

2
0

3
2
2
sinx
cosx
tanx
Evaluate the following using the process described above. Leave answers in simple
radical form if necessary.
11
4
1) sin(570 )
2) cos 
4) sec(90 )
5) csc(-270 )
7) cot
15
6
8) cos
27
6
3) cot
6) sin(-750 )
9)
A similar type of example:
10)
Find the value of the other trigonometric functions if:
sin   
5
, 90    90
13
HW: Unit Circle Practice WS
7
6
sec
11
4