Homework Questions
Unit Circle Quiz 1
You have 3 minutes!
Section 4.4
Graphing sin(x) and cos(x)
Periodic:
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A function is periodic if for some real
number α, f (x+ α) = f (x) for each x
in the domain.
The least positive value for α for which
f (x+ α) = f (x) is the period of the
function.
Examples…
Graph on your calc:
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y = sin(x) and determine if periodic
(ZOOM – TRIG)
Properties of sin(x)
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Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]
X-intercepts: nπ, where n=integer
Y-intercept: 0
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Max values: y=1 where x   2n
2
Min values: y= -1 where
3
x 
 2n
2
Example
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Find
9
2
by looking at the graph
Just like going around the unit circle
twice and then back to  2
Example
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Find the values of Ө where sin Ө = 0
Another Example
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1
sin  
2
Graph
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y = sin x for 3π ≤ x ≤ 5π
Graph cos x
Graph cos x
Properties of cos(x)
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Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]
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X-intercepts:
, where n=integer
2
Y-intercept: 1
Max values: y=1 where x  n n is even
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Min values: y= -1 where
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x  n
n is odd
Determine y=sin x,
y=cos x, or neither
 9
 7
Homework
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Worksheet