1. Introduction to College Algebra & Trigonometry
Algebra and Trigonometry
Chapter 6 – Trigonometry
Section 6.3 – Trigonometric Functions of Any Angle

2. Section 6.3 – Trigonometric Functions of Any Angle
Let be an angle in standard position with (x, y) a point on the terminal side of and r y x

3. Section 6.3 – Trigonometric Functions of Any Angle
Example:
(-5,12) 13 12 -5

4. Section 6.3 – Trigonometric Functions of Any Angle
You try: Determine the exact values of the six trigonometric functions of the angle in standard position whose terminal side contains the point (-3, -7).

5. Section 6.3 – Trigonometric Functions of Any Angle
Signs of Trig Functions
Quadrant II
Quadrant I S A T C
Quadrant III
Quadrant IV

6. Section 6.3 – Trigonometric Functions of Any Angle
You try:

7. Section 6.3 – Trigonometric Functions of Any Angle
Reference angles – the acute angle formed by the terminal ray and the x-axis.

8. Section 6.3 – Trigonometric Functions of Any Angle
You try: Find the reference angle for

9. Section 6.3 – Trigonometric Functions of Any Angle
Evaluating Trig. Functions of Any Angle
To find the value of a trig. Function of any angle,
Determine the function value for the associated reference angle;
Depending on the quadrant in which the original angle lies, affix the appropriate sign to the function value.

10. Section 6.3 – Trigonometric Functions of Any Angle
You try:
Evaluate

11. Section 6.3 – Trigonometric Functions of Any Angle
You try: Find two values of
that satisfy the equation
Do not use you calculator.

12. Section 6.3 – Trigonometric Functions of Any Angle
Using a calculator to solve or evaluate trig functions
To evaluate csc, sec & cot using the calculator, use the appropriate reciprocal function.

13. Section 6.3 – Trigonometric Functions of Any Angle
Using a calculator to solve or evaluate trig functions
To solve for the missing angle, use the inverse trig function keys.

14. Section 6.3 – Trigonometric Functions of Any Angle
You try:
Solve the equation
for

15. Section 6.3 – Trigonometric Functions of Any Angle
You try:
Solve the equation
for

16. Section 6.3 – Trigonometric Functions of Any Angle
You try:
Solve the equation
for

17. Section 6.3 – Trigonometric Functions of Any Angle
Definition of a Periodic Function
A function f is periodic if there exists a positive real number p such that
for all x in the domain of f.
The smallest number p for which f is periodic is called the period of f.

18. Section 6.3 – Trigonometric Functions of Any Angle
Even and Odd Trigonometric Functions
The cosine and secant functions are even.
The sine, cosecant, tangent, and cotangent functions are odd.