1. Review of Trigonometry
Appendix D.3

2. After this lesson, you should be able to:
work in radian measure
find reference angles
use and recreate the unit circle to find trig values of special angles
recognize and sketch the graphs of sine, cosine and tangent
use the Pythagorean trig identities and reciprocal identities to simplify trig expressions
solve basic trig equations

3. Angles initial ray  on x-axis
terminal ray
Standard position of an angle
(0, 0) x
acute angles angles between 0 and /2 radians
obtuse angles angles between /2 and  radians
co-terminal angles angles that share the same terminal ray
Ex: /2 and -3/2

4. Measuring Angles Positive angles measured counterclockwise
Negative angles measured clockwise

5. Radian Measure
Radian measure of a central angle in the unit circle is the length of the arc of the sector.
The length of the sector
r = 1 
Unit circle r 
s = r
circle with radius r
Arc Length is

6. Definitions of Trig Functions x y r
(x,y)
Circular Function Definitions

7. Quadrant Signs for Trig Functions
Quad II: Sine and cosecant are +
Quad I: All trig functions are +
Quad III: Tangent and cotangent are +
Quad IV: Cosine and secant are +

8. Common 1st Quadrant Angles
Degrees 0°
30°
45°
60°
90°
Radians
Sin 
Cos 
Tan 

9. Unit Circle Function Definitions 1 y  x
r = 1
Unit circle

10. Unit Circle with Special Angles
0° 
360 ° 
30 ° 
45 ° 
60 ° 
330 ° 
315 ° 
300 ° 
 120 °
 135 °
 150 °
 240 °
 225 °
 210 °
 180 °
90 ° 
270 °  
For  a positive angle.
r = 1
Remember: x = cos, y = sin

11. Reciprocal Identities

12. Trigonometric Identities & Formulas
Note: Those written in blue should be memorized.

13. Graph of Sine
Graph the function y = sin x over the interval [-2, 2]. State its amplitude, period,domain and range. x y

14. Graph of Cosine
Graph the function y = cos x over the interval [-2, 2]. State its amplitude, period,domain and range. x y

15. Graph of Tangent
Graph the function y = tan x over the interval [-2, 2]. State its period,domain and range. x y

16. Practice with Conversions
Example: Convert 850° to exact radian measure.
Example: Convert -34/15 to degree measure.

17. Practice with Trig Functions
Example: Given a point on the terminal side of  in standard position, find the exact value of the six trig. functions of .
P (-4, -3)

18. Practice with Trig Functions
Example: Given the quadrant and one trigonometric function value of  in standard position, find the exact value of the other five trig. functions.
A. Quadrant I; tan  = 5

19. Practice with Trig Functions
B. Quadrant III; cot  = 1

20. Solving Basic Trig Equations
Example 1 Solve the equation without using a calculator.

21. Solving Basic Trig Equations
Example 2 Solve the equation without using a calculator.

22. Homework Exercises for Appendix D.3: #1-7 all, 11-19 all, 27-35 odd
Appendix D.3 can be found online at the textbook site and also on the CD provided with your text.