1. Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians
Find the complement of θ, expressed in both degrees and radians
Find the supplement of θ, expressed in both degrees and radians
Find two angles that are coterminal to θ, expressed in both degrees and radians

2. Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians
complement of θ:
supplement of θ:
two angles coterminal to θ:

3. Homework Questions

4. Making Waves Activity
You have 45 minutes for the “Making Waves” activity.
Work in your assigned seat.
Work with your partner, but each of you must complete your own.

5. Trigonometric Functions: The Unit Circle
Section 4.2

6. Unit Circle A unit circle is a circle with radius = 1
The center of a unit circle is at the origin of a rectangular coordinate system (x-y plane)
The equation of a unit circle is
The point on the unit circle at angle θ corresponds to sine and cosine of θ

9. All Students Take Calculus

10. The Six Trigonometric Functions
Name
Abbreviation
Relation to (x, y)
Restriction
Sine
sin
y/1=y
Cosine
cos
x/1=x
Tangent
tan
y/x
x≠0
Cosecant
csc
1/y
y≠0
Secant
sec
1/x
Cotangent
cot
x/y

13. Warm-Up: February 5, 2016 Consider θ =135˚ Convert θ into radians
Find the complement of θ, expressed in both degrees and radians
Find the supplement of θ, expressed in both degrees and radians
Find two angles that are coterminal to θ, expressed in both degrees and radians

14. Warm-Up: February 5, 2016 Consider θ =135˚ Convert θ into radians
complement of θ:
supplement of θ:
two angles coterminal to θ:

15. Homework Questions?

16. Trig Function Relationships

17. Example 1
Determine the value of the six trigonometric functions of 240˚. You may not use a calculator.

18. You-Try #1
Determine the value of the six trigonometric functions of 135˚. You may not use a calculator.

19. You-Try #2
Determine the value of the six trigonometric functions of π. You may not use a calculator.

20. Even and Odd Cosine and Secant are even.
cos −𝜃 = cos 𝜃
sec −𝜃 = sec 𝜃
Sine, Cosecant, Tangent, and Cotangent are odd.
sin −𝜃 =− sin 𝜃
csc −𝜃 =− csc 𝜃
tan −𝜃 =− tan 𝜃
cot −𝜃 =− cot 𝜃

21. You-Try #4
Show two different ways to find sin − 𝜋 3 with the unit circle. You may not use a calculator.

22. Pythagorean Identities
Using and
we can get the following identities.

23. Example 6
Given that and
find the value of the rest of the trigonometric functions

24. You-Try #6 Given that and
find the value of the rest of the trigonometric functions

25. Cofunctions (Section 4.3)
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

26. Example 4 (Section 4.3)
Find a cofunction with the same value as the given function.

27. You-Try #4 (Section 4.3)
Find a cofunction with the same value as the given function.

28. Trig Functions Values Table

29. Assignments Read Section 4.2
Page 450 #1-25 Every Other Odd, # Odd
Page 462 #21-27 odd
No calculators!