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```Mr. Markwalter
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Start new unit
Return projects/tests
Oh? So you’re starting a new unit?
Three is the bee’s knees.
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We have seen sine and cosine graphs
Now, we will look at our other 4 functions
Why?
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We have seen sine and cosine graphs
Now, we will look at our other 4 functions
Why?
To get ready for solving bigger trig problems.
For example…
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The hot-air balloon festival held each year in
Phoenix, Arizona, is a popular event for
photographers. Jo Silver, an award-winning
photographer at the event, watches a balloon
rising from ground level from a point 500
feet away on level ground. Write the angle of
elevation as a function of the height of the
balloon.
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We need to get a grasp of our other functions
(not as long a unit as last time).
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The graphs we have seen of sine and cosine
functions have some similarities.
Let’s name some.
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A lot of these are obvious from the graphs.
Let’s see some.
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Now, if I wanted to make sin(x) become
cos(x), what would I need to do to the graph?
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Shift it to the left.
How much?
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π/2
And how would we do that?
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cos(x)=sin(x+π/2)
Sine and cosine can be interchanged!
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How would we get cos(x) to be sin(x)?
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sin(x)=cos(x-π/2)
Write the following cosine function as a sine
function.
f(x)=3cos(x)-2
Write the following cosine function as a sine
function.
f(x)=3cos(x)-2
To go from cos(x) to sin(x), add π/2 inside the
argument.
g(x)=3sin(x+ π/2)-2
Write the following sine function as a cosine
function.
f(x)=-2sin(x)+1
Write the following sine function as a cosine
function.
f(x)=-2sin(x)+1
To go from sin(x) to cos(x), subtract π/2 inside
the argument.
g(x)=-2cos(x- π/2 )+1
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Come get a whiteboard and a marker.
Nice a calm!
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Copy down the problem in your notebook.
Solve it there.
This can be a resource for going back for
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Given the function, rewrite it as an equivalent
sine or cosine function.
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What we are doing is REALLY shifting the
graph a QUARTER OF A PERIOD.
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You need to first figure out the period!
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Write h(x)=3cos(2πx) as a sine function.
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Write h(x)=3cos(2πx) as a sine function.
Find the period.
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Write h(x)=sin(π/2 x)-4 as a cosine function.
Find the period.
Subtract one fourth of it.
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Write h(x)=-2cos(π/4x)+2 as a sine function.
Find the period.
Find ¼ of the period.
Don’t forget the parentheses!
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Take in out and let’s practice!
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In general, looked ok.
I put a score out of 16 on your rubric.
Everyone got the same score UNLESS I noted
something differently on the evaluation YOU
handed in.
If you have questions, find me.
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1st period average: 68.6%
3rd period average: 69.1%
6th period average: 64.7%
Now, clearly there is room for improvement.
Changes to make ups.