College Algebra & Trigonometry, 2018a

428 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
Along the x-axis, the period for the graph will be 2π B =2π 3
, since the coefficient B
in this problem is 3. To find the new starting point, we’ll take the argument of the
cosine function and set it equal to zero.
3x − π =0
3x = π
x = π∗ 1 3 =π 3
So, our new starting point will be at π 3
. To determine the other critical values
along the x-axis, we can find out how far each “jump” between the critical values
would be. To do this, we take the period ( 2π 3
) and divide it by 4 (or multiply by
1
4 ). 2π
3 ∗1 4 =2π 12 =π 6
Now we can add this value to our new starting point four times to determine the
other critical values along the x-axis.
π
3 +π 6 =2π 6 +π 6 =3π 6 =π 2
3π
6 +π 6 =4π 6 =2π 3
4π
6 +π 6 =5π 6
5π
6 +π 6 = π
So the critical values along the x-axis would be:
2π
6 , 3π 6 , 4π 6 , 5π 6 , and 6π 6
or
π
3 , π 2 , 2π 3 , 5π 6 , and π