Download 4.2--Day 3---Domain and Period of Sine and Cosine

4.2--Day 3---Domain and Period of Sine and Cosine
What you should learn: To evaluate trigonometric functions using
the unit circle, to use domain and period to evaluate sine and
cosine functions, and use a calculator to evaluate trigonometric
functions.
Why you should learn it: Trigonometric functions have many
real-world applications.
Domain and Period of Sine and Cosine
The domain of sine and cosine functions is the set of _____
_________ ___________. Which means we can put any
value in for θ. Why is that?
The range are the values we get out which depend on our unit
circle since all the angle values occur in the unit circle.
From our unit circle:
Since in a unit circle
we can say
Therefore for Sine and Cosine:
Domain:
Range:
We know that the sine and cosine values repeat every 2π or
360o. Because this happens we say that these functions are
____________.
The ________ is the degree or radian value it takes before
the cycle starts to repeat itself.
Sine and Cosine are periodic and their period is _____. The
other 4 trig functions are periodic also, but we will look at
them later.
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EX: Evaluate ( if possible)­­­use the period of sine and cosine to help
EX: Evaluate (if possible) the six trigonometric functions of the real number.
EX: Use a calculator to evaluate the expression. Round to four decimal places.
MODE ON CALCULATOR!!!
HW: p. 377 13­37 odd, 45­53 odd = 18 problems
Try to figure problems out without looking at unit circle­­just use special triangles and converting to degrees
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