Download Day 1- Special Angles.notebook

Day 1­ Special Angles.notebook
October 31, 2014
4.1
Special Angles
Learning Goal: To be able to determine the primary trigonometric measure for any special angle from 0o to 360o
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Day 1­ Special Angles.notebook
October 31, 2014
CAST Rule
Quad 1
Quad 2
S
A
x
T
Quad 3
C
Quad 4
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Day 1­ Special Angles.notebook
October 31, 2014
Angles in Standard Position
Quad 1
Quad 2
(x,y)
terminal arm
θ
drop vertical line to form triangle with x axis
x
reference angle
Quad 3
Quad 4
Positive angles are formed when rotating counter clockwise from the +ive axis, always draw triangle with the x­axis. You always move counter­clockwise to the terminal arm.
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Day 1­ Special Angles.notebook
October 31, 2014
How to Use a Unit Circle to find the trig ratios for any angle?
A Unit Circle is a circle with centre at the origin and radius of 1 unit.
y
1
(x, y)
­1
0
Sin θ = y
Cos θ = x
θ
1
x
­1
Tan θ = y/x
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Day 1­ Special Angles.notebook
October 31, 2014
How to Use Special Triangles
45o
√2
1
45o
30o
2
√3
1
Sin 45 =
Cos 45 =
Tan 45 =
60o
1
Sin 30 = Sin 60 = Cos 30 =
Cos 60 =
Tan 30 =
Tan 60 =
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Day 1­ Special Angles.notebook
October 31, 2014
Now Let's Apply Special Triangles to Unit Circle
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Day 1­ Special Angles.notebook
October 31, 2014
Success Criteria:
• can determine any primary trigonometric ratio for 0, 30, 45, 60, 90 degrees and any multiple of those values
• can use a unit circle to find trig ratios for angles greater 90
• knows that the coordinates of a point (x,y) on a unit circle are related to the angle such that x=cos and y = sin and tan = y/x OR tan = sin/cos
• understands how to use the special triangles to determine trig ratios for 45, 30 and 60 degrees
• understands how to represent an angle as an exact trig ratio.
Homework (refer to text pg 22­227 to help if needed)
Pg 228 Communicate Your Understanding C2 & C3
Pg 228 Practise 1­5, 9, 10, 11, 12
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Day 1­ Special Angles.notebook
October 31, 2014
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