College Algebra & Trigonometry, 2018a

400 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
Likewise, the graph of y = − cos x begins at the minimum value before crossing
through 0 and going to the maximum value, back through 0 and ending at the
minimum value again.
1
1
2
zero
0
π
2
− 1 2
−1
minimum
maximum
π
zero
3π
2
2π
minimum
y = − cos x
Period
The period of the graph refers to how long it takes the graph to complete one full
cycle of values. In the standard sine and cosine functions, the period is 2π radians.
The function completes a single “wave” and returns to its starting place between
0 and 2π. A coefficient in front of the variable in a sine or cosine function will
affect the period of the graph. In the general expression y = A sin Bx, the value
of A affects the amplitude of the function and the value of B affects the period of
the function.
If we examine the table of values for the standard sine function, we can see how
the coefficient of the x-variable will affect the period of the graph. Starting with
the table from the standard sine function: