Download Unit 10B Notes: Coordinate Plane Trigonometry

Algebra 2A
Unit 10B Notes: Coordinate Plane Trigonometry
Name________________________ ______
Date_______ ______
Day 4: Angles of Rotation (10.2)
• With right triangle trig, we examined trig functions for angles in a right triangle – angles less than 90°.
• We can evaluate trig functions for other types of angles – angles 90° or larger and even negative angles.
• To do this, we are going to look at angles on a coordinate plane.
Angles in Standard Position: _______________________________________________________________
•
¼ rotation: ________
•
½ rotation: ________
•
¾ rotation: ________
•
1 full rotation: _______
Example #1: Draw an angle with the given measure in standard position.
A. 320°
B. –110°
C. 990°
Coterminal Angles: _______________________________________________________________________
How to find coterminal angles:
Example #2: Find the measures of a positive angle and a negative angle that are coterminal with each given angle.
A. θ = 65°
B. θ = 410°
C. θ = –150°
Reference Angles: _________________________________________________________________________
How to find reference angles:
Example #3: Find the measure of the reference angle for each given angle.
A. θ = 135°
B. θ = –105°
C. θ = 325°
Using Trig Functions for ANY Angle:
•
Create a “reference triangle” with the reference angle
Example #4: P(–3, 6) is a point on the terminal side of in standard position.
Find the exact value of the six trigonometric functions for .
y
x
Practice Problems
Draw an angle with the given measure in standard position.
1. –120°
2. 240°
3. –585°
Find the measures of a positive angle and a negative angle that are coterminal with each angle.
4. θ = 515°
5. θ = −93°
6. θ = 162°
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Find the measures of the reference angle for each given angle.
7. θ = 211°
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10. θ = 119°
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8. θ = −55°
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11. θ = −160°
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9. θ = 555°
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12. θ = 435°
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P is a point on the terminal side of  in standard position. Find the exact value of the six trigonometric functions for 13. P(−5, 5)
14. P(12, –9)
15. P(−7, −5)
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Day 5: Radians & The Unit Circle (10.3)
Radian:
Example #1: Convert each angle from degrees to radians
A. 60°
B. –240°
C. 160°
Example #2: Convert each angle from radians to degrees
A.
4
3
B. 2
Unit Circle:
• Yesterday, we used points on a coordinate plane to find values
of trigonometric functions for any angle measure.
•
Today we will focus on trigonometric values for special angles.
•
We will use a Unit Circle, or a circle with a radius of 1, to
model these special angles.
On the Unit Circle…
Cos = __________
Sin = __________
Tan = __________
C.
5
6
Filling in the Unit Circle:
Using the Unit Circle:
Practice: Find the exact value of each trigonometric function using the unit circle.
1. sin 30°
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4. cos 330°
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7. cos
2π
3
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10. sin 315°
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13. cos
5π
3
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16. cos –270°
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2. cos 45°
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5. sin 150°
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8. tan
5π
4
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11. cos 225°
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14. sin −
π
6
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17. sin –225°
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3. tan 60°
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6. tan 210°
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9. tan
5π
6
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12. tan 270°
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15. tan π
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18. sin 2π
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Day 6: Graphs of Sine and Cosine (11.1)
Warm Up: Using your Unit Circle, fill in the table below using the decimal approximation for each value.
Round your values to the nearest hundredth.
Graph: f(θ) = sinθ
(θ , sinθ)
Graph: f(θ) = cosθ
(θ , cosθ)
Properties of Parent Sine and Cosine Graphs:
•
Periodic Function:
f(θ) = sinθ
f(θ) = cosθ
Domain
Range
Period
Exploring Tranformations:
Using your graphing calculator (in radian mode) and what you know about translations and
stretches/compressions, describe the transformations to the graphs of the sine equations below:
**Use ZoomTrig to get an appropriate viewing window**
1. f(θ) = 2sinθ
2. f(θ) = sin2θ
3. f(θ) = sinθ + 2
4. f(θ) = sin(θ + 2)
5. f(θ) = –sinθ
Predicting Equations:
Write an equation that describes the given transformation of the parent function f(θ) = sinθ, then use your
graphing calculator to check your prediction.
6. Vertical translation down 1
7. Vertical stretch by a factor of 4
8. Horizontal translation right 3
9. Horizontal stretch by a factor of 2
10. Reflection over the x-axis and a vertical stretch by a factor of 3