1. 6.4 - Trig Ratios in the Coordinate Plane
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6.4 - Trig Ratios in the Coordinate Plane

2. 6.4 - Trig Ratios in the Coordinate Plane
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6.4 - Trig Ratios in the Coordinate Plane

3. Trig Ratios in the Coordinate Plane
Section 6.4
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6.4 - Trig Ratios in the Coordinate Plane

4. 6.4 - Trig Ratios in the Coordinate Plane
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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6.4 - Trig Ratios in the Coordinate Plane

5. 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 𝒓= 𝒙 𝟐 + 𝒚 𝟐
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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6.4 - Trig Ratios in the Coordinate Plane

6. 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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6.4 - Trig Ratios in the Coordinate Plane

7. 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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6.4 - Trig Ratios in the Coordinate Plane

8. 6.4 - Trig Ratios in the Coordinate Plane
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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6.4 - Trig Ratios in the Coordinate Plane

9. 6.4 - Trig Ratios in the Coordinate Plane
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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6.4 - Trig Ratios in the Coordinate Plane

10. 6.4 - Trig Ratios in the Coordinate Plane
Example 2
Let 𝟏𝟎 𝟏𝟎 ,− 𝟑 𝟏𝟎 𝟏𝟎 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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6.4 - Trig Ratios in the Coordinate Plane

11. 6.4 - Trig Ratios in the Coordinate Plane
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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6.4 - Trig Ratios in the Coordinate Plane

12. Finding the Exact Value Without a Calculator
Make sure the calculator is set in RADIAN mode
Apply all three trig functions
Determine which quadrant it belongs to identify the quadrant of the terminal side
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6.4 - Trig Ratios in the Coordinate Plane

13. 6.4 - Trig Ratios in the Coordinate Plane
Example 3
Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for − 𝟏𝟏 𝟓 𝝅
Quadrant I (+, +)
Quadrant II (– , +)
Quadrant IV (+, –)
Quadrant III (–, –)
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6.4 - Trig Ratios in the Coordinate Plane

14. 6.4 - Trig Ratios in the Coordinate Plane
Example 4
Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for 𝟖 𝑹𝒂𝒅𝒊𝒂𝒏
Quadrant I (+, +)
Quadrant II (– , +)
Quadrant IV (+, –)
Quadrant III (–, –)
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6.4 - Trig Ratios in the Coordinate Plane

15. 6.4 - Trig Ratios in the Coordinate Plane
Your Turn
Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for −𝟐𝟑𝝅
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6.4 - Trig Ratios in the Coordinate Plane

16. 6.4 - Trig Ratios in the Coordinate Plane
Assignment
Pg 452
1-9 odd (List all 6 Trig Functions)
15-23 odd
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6.4 - Trig Ratios in the Coordinate Plane