Unit Circle - Miss Holdman's Math Classes · 2018-09-07 · 1-UnitCircleNotes.doc . Unit Circle...
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solutionstomath at tinyurl.com/solutionstomath Unit Circle 3 2 , 1 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 2 , 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 2 , 3 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 3 2 , 1 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 2 2 , 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 1 2 , 3 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 3 2 , − 1 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 2 2 , − 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 1 2 , − 3 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 2 , − 3 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 2 , − 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 3 2 , − 1 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1,0 ( ) -1,0 ( ) 0,1 ( ) 0, −1 ( ) 0° 30° 45° 60° 120° 135° 150° 90° 180° 210° 225° 240° 270° 300° 315° 330° 0 π π 6 π 4 π 2 π 3 3 π 4 2π 3 5 π 6 7π 6 5 π 4 4π 3 3 π 2 5 π 3 7π 4 11 π 6 360° 2π Quad 4: Points: ( +, –) Radians: the numerator is one less than the twice denominator Trig: sin: – cos: + tan: – Quad 1: Points: (+, +) Trig: sin: + cos: + tan: + Quad 3: Points: (–, –) Radians: the numerator is one more than the denominator Trig: sin: – cos: – tan: + Quad 2: Points: (–, +) Radians: the numerator is one less than the denominator Trig: sin: + cos: – tan: –
Transcript of Unit Circle - Miss Holdman's Math Classes · 2018-09-07 · 1-UnitCircleNotes.doc . Unit Circle...
solutionstomath at tinyurl.com/solutionstomath
Unit Circle
32
,12
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2
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−
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1,0( )
-1,0( )
0,1( )
0,−1( )
0°
30°
45° 60° 120°
135°
150°
90°
180°
210°
225°
240°
270°
300°
315°
330°
0 π
π6
π4
π2
π3
3π4
2π3
5π6
7π6
5π4
4π3
3π2
5π3
7π4
11π6
360° 2π
Quad 4: Points: ( +, –) Radians: the numerator is one less than the twice denominator Trig: sin: – cos: + tan: –
Quad 1: Points: (+, +) Trig: sin: + cos: + tan: +
Quad 3: Points: (–, –) Radians: the numerator is one more than the denominator Trig: sin: – cos: – tan: +
Quad 2: Points: (–, +) Radians: the numerator is one less than the denominator Trig: sin: + cos: – tan: –
solutionstomath at tinyurl.com/solutionstomath
Unit Circle
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, ⎛
⎝⎜⎞⎠⎟
, ⎛
⎝⎜⎞⎠⎟
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, ( )
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_____°
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Gemma Holdman
Gemma Holdman
Gemma Holdman
A unit circle is a circle of radius 1, with its center at the origin of a rectangular coordinate system. Having knowledge of the unit circle is helpful in trigonometry, geometry, and pre-calculus. It makes learning some mathematical concepts much easier. Please hold on to this!
solutionstomath at tinyurl.com/solutionstomath
Unit Circle
___
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⎝⎜⎞⎠⎟
, ⎛
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solutionstomath at tinyurl.com/solutionstomath
Unit Circle
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solutionstomath at tinyurl.com/solutionstomath
Unit Circle
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1-UnitCircleNotes.doc
Unit Circle Notes Divide everything by 12:
o Degrees: Each angle is 30° (360°/12 = 30° or the right angle divided by 3) Patterns with degrees: since we are adding 30, use multiples of 30 (or 3 then add a zero)
o Radians:
Each angle is
π6
2π12
=π6
⎛⎝⎜
⎞⎠⎟
. To get the following angles, add 1/6 to the previous angle
and reduce or: • First label the right angles: pi/2, pi, 3pi/2, and 2 pi then • pi/6, 2pi/6 (reduce), 3pi/6 (skip), 4pi/6 (reduce), 5pi/6, 6pi/6 (skip), 7pi/6, 8pi/6
(reduce), 9pi/6 (skip), 10pi/6 (reduce), 11pi/6, 12pi/6 (skip) Divide everything by 8:
o Degrees: Each angle is 45° (360°/8 = 45° or the right angle divided by 2)
o Radians:
Each angle is
π4
2π8
=π4
⎛⎝⎜
⎞⎠⎟
. To get the following angles, and 1/4 to the previous angle
and reduce or:
• First label the right angles: pi/2, pi, 3pi/2, and 2 pi then • pi/4, 2pi/4 (skip), 3pi/4, 4pi/4 (skip), 5pi/4, 6pi/4 (skip), 7pi/4 and 8pi/4 (skip)
Points:
• Combine: notice the numerator gets bigger for the y-points in the first quadrant: compare: • Flip everything (points and denominator for the radians) to the left then everything down • Quadrants (+, +), (-, +), (-,-), (+, -)
What patterns do you see with the numerator and denominator of the radians in quadrant 2, 3 or 4? Quadrant 2: numerator is one less than the denominator Quadrant 3: numerator is one more than the denominator Quadrant 4: numerator is one less than twice the denominator Also, use reflections over the x- and y-axis for the denominator
