Do Now A 22 foot extension ladder leaning

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

Section 1. 3 Trigonometric Functions Objective: SWBAT use trigonometric functions in the coordinate plane.

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 •

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

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

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

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 .

Example 2 Cntd. 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 .

Example 3 Cntd. FINDING FUNCTION VALUES OF AN ANGLE

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 + 2 y = 0, x ≥ 0. We can use any point on the terminal side of to find the trigonometric function values. Choose x = 2.

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.

Homework Page 24 -25 # 6, 8, 10, 12, 26, 28