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UNIT CIRCLE and Trigonometry Graphing
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Terms in this set (78)
Unit Circle
sin x
Give radians and ordered pair for 0º
0 (1,0)
cos x
Give radians and ordered pair for 30º
π/6 (√3/2, 1/2)
tan x
Give radians and ordered pair for 45º
π/4 (√2/2, √2/2)
csc x
sec x
Give radians and ordered pair for 60º
π/3 (1/2, √3/2)
Give radians and ordered pair for 90º
π/2 (0,1)
cot x
Give radians and ordered pair for 120º
2π/3 (-1/2, √3/2)
range of sin
[-1,1]
Give radians and ordered pair for 135º
3π/4 (-√2/2, √2/2)
domain of cos
(-∞,∞)
Give radians and ordered pair for 150º
4π/5 (-√3/2, 1/2)
domain of tan
All angles x except π/2 ± πn for all integers n
range of csc
(−∞,−1]∪[1,∞]
Give radians and ordered pair for 180º
π (-1,0)
Give radians and ordered pair for 210º
7π/6 (-√3/2, -1/2)
tan y-int
(0,0)
Give radians and ordered pair for 225º
5π/4 (-√2/2, -√2/2)
csc y-int
none
Give radians and ordered pair for 240º
4π/3 (-1/2, -√3/2)
Period Function
A function that repeats at regular intervals.
Give radians and ordered pair for 270º
3π/2 (0, -1)
Cycle
The shortest repeating interval.
Give radians and ordered pair for 300º
5π/3 (1/2, -√3/2)
Period
The horizontal length of one cycle.
Give radians and ordered pair for 315º
7π/4 (√2/2, -√2/2)
Sinusoidal Functions
Sine and cosine are often referred to as ????.
Give radians and ordered pair for 330º
11π/6 (√3/2, -1/2)
Amplitude or vertical stretch factor
Half the difference between the maximum and minimum y-values of the graph of a sine or cosine function is called the ??? of the graph or wave.
Give radians and ordered pair for 360º
2π (1,0)
Phase shift
In a sinusoidal function, a horizontal translation is often called a ???
0° is ? radians
0π
2π/|b|
Period of Cos and Sin=
Frequency
Sometimes the horizontal axis has units of time on it such as seconds, minutes, etc. With these types of problems, we are often interested in how many cycles completed during that unit of time, which is also known as the ???
30° is ? radians
π/6
45° is ? radians
π/4
y= asinb(x-c)+d
graphing form of sine.
60° is ? radians
π/3
vertical translation
is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.
90° is ? radians
π/2
π/|b|
Period of Tangent
120° is ? radians
2π/3
Tangent
??? does not have amplitude
135° is ? radians
3π/4
π
The period for tangent is ?? and not the same as it was for the sine and cosine functions.
150° is ? radians
5π/6
180° is ? radians
π
210° is ? radians
7π/6
225° is ? radians
5π/4
240° is ? radians
4π/3
270° is ? radians
3π/2
300° is ? radians
5π/3
315° is ? radians
7π/4
330° is ? radians
11π/6
360° is ? radians
2π
csc(30°)
2
cos(45°)
√2/2
sin(60°)
√3/2
cos(0°)
1
cos(300°)
1/2
sin(180°)
0
sin(210°)
−1/2
sin(225°)
−√2/2
cos(150°)
−√3/2
sin(270°)
−1
csc(135°)
√2
sec(225°)
-√2
sec(300°)
−2
tan(90°)
undefined
What are the signs of an ordered pair in QI
(+, +)
What are the signs of an ordered pair in QII
(-, +)
What are the signs of an ordered pair in QIII?
(-, -)
What are the signs of an ordered pair in QIV?
(+, -)
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