1. Warm Up
Find the reciprocal of each integer:
6 7
1 2 7
1 8
5 4

2. Using Definitions of the Trigonometric Functions
Section 1.4
Using Definitions of the Trigonometric Functions
SWBAT:
Give the signs of the six trigonometric functions for a given angle.
Identify the quadrant or quadrants for angles satisfying given conditions.

3. Reciprocal Identities

4. Using the Reciprocal Identities
Find each function value.
Find cos  if sec  =
Find sin  if csc 
Find cos  if sec  = 5 3
Find sin θ if csc θ = −√12 2

5. Signs & Ranges of Function Values
Remember: r is the distance from the origin to a point (x, y) . Distance is never negative so r >0. If we find the six trigonometric functions of an angle θ in quadrant I, (x, y) are both positive an so are all 6 fucntions. What happens if we have a point in a different quadrant?!?

6. Signs & Ranges of Function Values
All Students Take Calculus

7. Signs & Ranges of Function Values
 in Quadrant
sin 
cos 
tan 
cot 
sec 
csc  I + + + + + + +  II  +
III  + IV

8. Identifying Quadrants
Identify the quadrant (or quadrants) of any angle θ that satisfies:
sin θ > 0 and tan θ < 0
cos  > 0 and sec  < 0
sin  > 0 and cos  < 0
csc  < 0 and sec  < 0
tan > 0

9. Identifying Quadrants
Give the signs of the six trigonometric functions for each of the following angles:
74 
183 
302 
406 
-121 

10. Ranges of Trigonometric Functions

11. DECIDING WHETHER A VALUE IS IN THE RANGE OF A TRIGONOMETRIC FUNCTION
Decide whether each statement is possible or impossible.
(a) sin θ = 2.5
Impossible
(b) tan θ =
Possible
(c) sec θ = .6
Impossible

12. FINDING ALL FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT
Suppose that angle  is in quadrant II and
Find the values of the other five trigonometric functions.
Let r = 3. Then y = 2.
What is x?
Use the Pythagorean Theorem…
Since  is in quadrant II,

13. Let r =3, y = 2, x = √5 Sin θ = Csc θ = Cos θ = Sec θ =
FINDING ALL FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT
Let r =3, y = 2, x = √5
Sin θ = Csc θ =
Cos θ = Sec θ =
Tan θ = Cot θ =
Remember to rationalize the denominator.

14. FINDING ALL FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT
Suppose that angle  is in quadrant II and
Find the values of the other five trigonometric functions.
Cos θ= −√3 4
Cos θ= −√3 4
Let r = 4. Then x = -√3
What is y?
Use the Pythagorean Theorem…

15. FINDING ALL FUNCTION VALUES GIVEN ONE VALUE AND THE QUADRANT
Sin θ = Csc θ =
Cos θ = Sec θ =
Tan θ = Cot θ =

16. Homework
Pages
# 4, 6, 28, 32, 34, 40, 48, 50