1. The Six Trig Functions Objective: To define and use the six trig functions

2. SOH CAH TOA We will start by looking at three of the trig functions: the sine, cosine, and tangent. We will use a right triangle to help define them.

3. SOH CAH TOA Each of these functions has a reciprocal function. The cosecant goes with the sine, the secant goes with the cosine, and the cotangent goes with the tangent.

4. Example 1 Lets look at the following triangle to find the values of the six trig functions.

5. Example 1 Lets look at the following triangle to find the values of the six trig functions. The first thing we need to do is use the Pythagorean Theorem to find the hypotenuse.

6. Example 1 Lets look at the following triangle to find the values of the six trig functions.

7. Example 1 You Try: Use the following triangle to find the value of all six trig functions. Again, you need to use the Pythagorean Theorem to find the missing side.

8. Example 1 You Try: Use the following triangle to find the value of all six trig functions.

9. Example 2 We will use our knowledge of a 45-45-90 triangle to find the sin, cos, and tan of a 45 0 angle. We will look at this on a unit circle (a circle with a radius of 1).

10. Example 2 We will use our knowledge of a 45-45-90 triangle to find the sin, cos, and tan of a 45 0 angle. We will look at this on a unit circle (a circle with a radius of 1).

11. Example 3 We will use our knowledge of a 30-60-90 triangle to find the sin, cos, and tan of a 30 0 and 60 0 angles. We will look at this on a unit circle.

12. Example 3 We will use our knowledge of a 30-60-90 triangle to find the sin, cos, and tan of a 30 0 and 60 0 angles. We will look at this on a unit circle.

13. Example 3 We will use our knowledge of a 30-60-90 triangle to find the sin, cos, and tan of a 30 0 and 60 0 angles. We will look at this on a unit circle.

14. Trig Identities We stated earlier that some functions were reciprocals of others. We will now look at them this way:

15. Trig Identities There are two more important identities that you need to know.

16. The Calculator Your calculator only has the sin, cos, and tan functions on it. To find the other three, you need to use your reciprocal relationships. Always make sure that when you are working in radians, your calculator is in radians.

17. The Calculator Your calculator only has the sin, cos, and tan functions on it. To find the other three, you need to use your reciprocal relationships. Find the We will look at this as

18. Angle of Elevation/Depression From the horizontal, looking up at an object is called the angle of elevation. From the horizontal, looking down at an object is called the angle of depression.

19. Example 7 A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3 0. How tall is the Washington Monument?

20. Example 7 A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3 0. How tall is the Washington Monument?

21. Example 8 An historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle between the bike path and the walkway.

22. Example 8 An historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle between the bike path and the walkway.

23. Example 9 Find the length of the skateboard ramp.

24. Example 9 Find the length of the skateboard ramp.

25. Homework Page 467-468 1, 3, 5, 9-25 odd, 57, 59, 61, 63, 65