1. Do Now
A 22 foot extension ladder leaning against a building makes a 70o angle with the ground. How far up the building does the ladder reach?

2. Section 1.3 Trigonometric Functions
Objective:
SWBAT use trigonometric functions in the coordinate plane.

3. Trigonometric Functions
Let (x, y) be a point other than the origin on the terminal side of an angle  in standard position. The distance from the point to the origin is

4. Trigonometric Functions
The six trigonometric functions of θ are defined as follows:

5. Finding Function Values Example 1
The terminal side of angle  in standard position passes through the point (12, 16). Find the values of the six trigonometric functions of angle .
(12, 16) 16 12 

6. Finding Function Values
x = 12 y = 16 r = 20

7. FINDING FUNCTION VALUES OF AN ANGLE
Example 2
FINDING FUNCTION VALUES OF AN ANGLE
The terminal side of angle  in standard position passes through the point (8, 15). Find the values of the six trigonometric functions of angle .

8. FINDING FUNCTION VALUES OF AN ANGLE
Example 2 Cntd.
FINDING FUNCTION VALUES OF AN ANGLE

9. FINDING FUNCTION VALUES OF AN ANGLE
Example 3
FINDING FUNCTION VALUES OF AN ANGLE
The terminal side of angle  in standard position passes through the point (–3, –4). Find the values of the six trigonometric functions of angle .

10. FINDING FUNCTION VALUES OF AN ANGLE
Example 3 Cntd.
FINDING FUNCTION VALUES OF AN ANGLE

11. Example 4
FINDING FUNCTION VALUES OF AN ANGLE
(If terminal ray is given as a line)
Find the six trigonometric function values of the angle θ in standard position, if the terminal side of θ is defined by x + 2y = 0, x ≥ 0.
We can use any point on the terminal side of  to find the trigonometric function values.
Choose x = 2.

12. FINDING FUNCTION VALUES OF AN ANGLE
Example 4 Cntd.
FINDING FUNCTION VALUES OF AN ANGLE
The point (2, –1) lies on the terminal side, and the corresponding value of r is
Multiply by to rationalize the denominators.

13. Homework
Page # 6, 8, 10, 12, 26, 28