1. Warm-Up: March 4, 2016
Find the exact value of cos sin −1 − 4 5

2. Homework Questions?

3. Right Triangle Trigonometry
Section 4.3

4. Right Triangles B c = length of the hypotenuse
A right triangle has a 90˚ angle and two acute angles B
c = length of the hypotenuse
a = length of side opposite of A, adjacent to B A C
b = length of side adjacent to A, opposite of B

5. Trigonometric Functions
SOH-CAH-TOA

6. More Trigonometric Functions

7. Example 1
Find the value of each of the trigonometric functions of θ. 3 4 c A B C θ

8. You-Try #1
Find the value of each of the trigonometric functions of θ. 5 12 c A B C θ

9. Pythagorean Triples
Pythagorean triples are integer side lengths of a right triangle
3-4-5
And many more
And any multiple of any of them
(such as )

10. Special Triangles

11. Trig Values of Special Angles
Degrees
Radians
sin
cos
tan
30˚
45˚
60˚

12. You-Try #2
Find the exact value of sin 𝜋 6 − cos 𝜋 4

13. Inverse Trig Functions
If sin 𝜃 =𝑥, then 𝜃= sin −1 𝑥
“Theta equals the inverse sine of x”
Other inverse trig functions follow the same format
TI-83: [2nd] [sin]

14. You-Try #3
Use a calculator to find the value of the acute angle 𝜃 to the nearest tenth of a degree.
cos 𝜃 =0.8771
tan 𝜃 =
Use a calculator to find the value of the acute angle 𝜃 in radians, rounded to three decimal places.
sin 𝜃 =0.9499
tan 𝜃 =0.5117

15. Assignment
Page 461 #1-19 odd
No calculator

16. First Few Problems B B 3) 29 9 θ A θ C 12 A C 21 5) B 26 10 θ A C
In Exercises 1-8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then, find the value of each of the six trigonometric functions of θ. 3) 21 29 A B C θ 9 12 A B C θ 1) 10 5) 26 A B C θ

17. Warm-Up:
Find the value of each of the trigonometric functions of θ. a 15 17 A B C θ

18. Homework Questions?

19. Unit Circle Quiz!
Clear everything off of your desk except a pencil and eraser.
5 minute time limit
All or nothing
Must be turned in by the end of 5 minutes
Do NOT begin until instructed to do so.
Any talking while any quiz is out will result in a zero.

20. Cofunctions
The value of a trig function of an angle is equal to the value of the cofunction of the complement of the angle
If θ is in radians, replace 90˚ with

21. Example 4
Find a cofunction with the same value as the given function.

22. You-Try #4
Find a cofunction with the same value as the given function.

23. Trig Functions on TI-83
All scientific and graphing calculators should have buttons for sin, cos, and tan.
Most do not have csc, sec, and cot.
Make sure that your calculator is set to the correct angle measure (degrees or radians)
TI-83: Press [MODE] and make sure the correct one of “Radian” or “Degree” is highlighted

24. Angles of Elevation & Depression
The angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is the angle of elevation.
The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is the angle of depression.
angle of depression

25. Example 5
Sighting the top of a building, a surveyor measured the angle of elevation to be 24˚. The transit is 5 feet above the ground and 250 feet from the building. Find the building’s height (to the nearest foot).

26. You-Try #5
At a certain time of day, the angle of elevation of the sun is 39˚. A tree casts a shadow 37 feet long. Find the tree’s height (to the nearest foot).

27. Assignment Read Section 4.3 Page 461 #1-19 odd Page 462 #29-49 odd
No calculator
Page 462 #29-49 odd
Calculator required

28. First Few Problems
In Exercises 21-28, find a cofunction with the same value as the given expression.

29. Warm-Up:
At a certain time of day, the angle of elevation of the sun is 59˚. A tree casts a shadow 24 feet long. Find the tree’s height (to the nearest foot).

30. Homework Questions?

31. Unit Circle Quiz!
Clear everything off of your desk except a pencil and eraser.
5 minute time limit
All or nothing
Must be turned in by the end of 5 minutes
Do NOT begin until instructed to do so.
Any talking while any quiz is out will result in a zero.

32. Unit Circle Quiz!
Clear everything off of your desk except a pencil and eraser.
5 minute time limit

33. Example 6
The Washington Monument is 555 feet high. If you stand ¼ mile away (1320 feet), and look at the top, what is the angle of elevation (to the nearest degree)?

34. You-Try #6
A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

35. Assignment Read Section 4.3 Page 461 #1-19 odd Page 462 #29-49 odd
No calculator
Page 462 #29-49 odd
Calculator required