1. Trigonometric Functions of Acute Angles
Demana, Waits, Foley, Kennedy
4.2
Trigonometric Functions of Acute Angles

2. What you’ll learn about
Right Triangle Trigonometry
Two Famous Triangles
Evaluating Trigonometric Functions with a Calculator
Common Calculator Errors when Evaluating Trig Functions
Applications of Right Triangle Trigonometry
… and why
The many applications of right triangle trigonometry
gave the subject its name.

3. Standard Position
An acute angle θ in standard position, with one ray along the positive x-axis and the other extending into the first quadrant.

4. Trigonometric Functions

5. Example: Evaluating Trigonometric Functions of 45º
Find the values of all six trigonometric functions for an angle of 45º.

6. Solution
Find the values of all six trigonometric functions for an angle of 45º.

7. Example: Evaluating Trigonometric Functions of 60º
Find the values of all six trigonometric functions for an angle of 60º.

8. Solution
Find the values of all six trigonometric functions for an angle of 60º.

9. Common Calculator Errors When Evaluating Trig Functions
Using the calculator in the wrong angle mode (degree/radians)
Using the inverse trig keys to evaluate cot, sec, and csc
Using function shorthand that the calculator does not recognize
Not closing parentheses

10. Example: Solving a Right Triangle

11. Solution

12. Terminology
Line of sight: The line from the eye of the observer to the object
Angle of elevation: Angle between the line of sight and the horizontal when the object is above the horizontal
Angle of depression: Angle between the line of sight and the horizontal when the object is below the horizontal

13. Word Problem 1
A giant redwood tree casts a shadow that is 452 feet long. Find the height of the tree if the angle of elevation of the sun is 12.30

14. Word problem solution

15. Example 2: A 40 foot ladder leans against a building
Example 2: A 40 foot ladder leans against a building. If the base of the ladder is 15 feet from the base of the building, what is the angle formed by the ladder and the building?
In relation to theta, which sides are we given?
How would you set up the equation?

16. Example 2: A 40 foot ladder leans against a building
Example 2: A 40 foot ladder leans against a building. If the base of the ladder is 15 feet from the base of the building, what is the angle formed by the ladder and the building?
40’
15’