5.2 Graphing Trig Functions
The Unit Circle
In order to graph trig functions we must first examine the unit circle. It is called the unit circle because it is a circle whose radius is 1 unit.
By drawing a radius anywhere in the unit circle you can create a right angled triangle to the x-axis.
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The
angle discussed here is always the one created between the
positive x-axis and the hypotenuse of the triangle in a
counter-clockwise direction. The coordinate of the point at the
circumference of the circle is always going to be
<GSP Demo for unit circle>
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We can plot the relation between the angle and the y-value on the unit circle to see what sine looks like for all values of θ.
<GSP Demo for sine, cosine>
Properties of Graphs of Sine and Cosine
Periodicity: Both Sine and Cosine are periodic functions (i.e. the graphs repeat themselves on a specific interval) What is the period of these functions?
Principal Axis: the mean value of the curve.
Amplitude:
the distance from the principal axis to the extrema. What is the
amplitude of
?
Graphs
in the form
:
What does a
change in the curve?
Graphs
in the form
:
What does b
change in the curve? Find an expression for the relationship between
the period and the b
value.
p. 531# 1-4
p. 534# 1-4, p. 535#1-2
p. 537# 1-4
.