1. 13.2 - Define General Angles and Radian Measure
Page 857 3) B 4) C 5) A 7) 9)
11)
13)
15)
430°, –290°
17)
235°, –405°
19)
π/2, –3π/2
21)
10π/9, –8π/9
23)
2π/9
25)
–13π/9
27)
20°
29)
900°
31) B
33)
S = 5π/4 m., A = 15π/8 m2
35)
S = 10π m., A = 60π m2
37)
430°, –290°
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Define General Angles and Radian Measure

2. Evaluating Trig Functions of Any Angle
Section 13.3
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Evaluating Trig Functions

3. 13.3 - Evaluating Trig Functions
Review
Determine the Trigonometric Functions for Ѳ 5 4 3
SIN ө= COS ө = TAN ө =
CSC ө = SEC ө = COT ө=
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Evaluating Trig Functions

4. Equation in Standard Form
For ө be an angle in standard position with any point (x, y)
SIN ө = y/r
COS ө = x/r
TAN ө = y/x
CSC ө = r/y
SEC ө = r/x
COT ө = x/y
B. To establish the radius, the equation is
C. Think of “ASTC: All Students Take Calculus”
A: All points are always positive in Quadrant I
S: Sine points are positive in Quadrant II
T: Tan points are positive in Quadrant III
C: Cosine points are positive in Quadrant IV
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Evaluating Trig Functions

5. Equation in Standard Form
For ө be an angle in standard position with any point (x, y)… S A
When ALL trig functions are positive
When SIN is positive
Quadrant II (– , +)
Quadrant I (+, +) T C
When TAN is positive
When COS is positive
Quadrant III (–, –)
Quadrant IV (+, –)
“All Students Take Calculus”
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Angles of Rotation

6. Steps in Evaluating Functions given a Point
Draw a picture from a coordinate plane
Identify and plot the point onto the coordinate plane
Determine the missing side using the radius equation
Use Trigonometric Functions to solve
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Evaluating Trig Functions

7. 13.3 - Evaluating Trig Functions
Example 1
Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 4 3
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Evaluating Trig Functions

8. 13.3 - Evaluating Trig Functions
Example 1
Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 3 4 5
SIN ө = COS ө = TAN ө =
CSC ө = SEC ө = COT ө =
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Evaluating Trig Functions

9. 13.3 - Evaluating Trig Functions
Example 2
Let (–3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө.
SIN ө = COS ө = TAN ө =
CSC ө = SEC ө = COT ө =
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Evaluating Trig Functions

10. 13.3 - Evaluating Trig Functions
Your Turn
Let (1, –1) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө.
SIN ө = COS ө = TAN ө =
CSC ө = SEC ө = COT ө =
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Evaluating Trig Functions

11. 13.3 - Evaluating Trig Functions
Reference Angles
Reference angles is a positive acute angle formed by the terminal side of ө and the x-axis. They are viewed as linear pairs. (Think: REFER’s back to the x-axis)
No reference trigonometric values of measure are greater than or equal to 90° or less than or equal to 0°
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Evaluating Trig Functions

12. 13.3 - Evaluating Trig Functions
Reference Angles
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Evaluating Trig Functions

13. 13.3 - Evaluating Trig Functions
Example 3
Given Ѳ = 135°, determine the reference angle for each given angle.
135°
45°
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Evaluating Trig Functions

14. 13.3 - Evaluating Trig Functions
Example 4
Given Ѳ = –105°, determine the reference angle for each given angle.
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Evaluating Trig Functions

15. 13.3 - Evaluating Trig Functions
Example 5
Given Ѳ = 88°, determine the reference angle for each given angle.
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Evaluating Trig Functions

16. 13.3 - Evaluating Trig Functions
Your Turn
Given Ѳ = 212°, determine the reference angle for each given angle.
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Evaluating Trig Functions

17. 13.3 - Evaluating Trig Functions
Assignment
Page 870
3-15 odd, all
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Evaluating Trig Functions