College Algebra & Trigonometry, 2018a

9.2. GRAPHING TRIGONOMETRIC FUNCTIONS 399
y =2sinx
2
maximum
1
zero
0
π
2
−1
zero
π
3π
2
zero
2π
−2
minimum
A negative value of the coefficient in front of a trigonometric function will not
change the Amplitude of the function, but it will change the shape of the function.
For example, the function:
y = − sin x
has an amplitude of 1, but the graph will be different from the graph y =sinx.
All of the y-values of the function y = − sin x will have the opposite sign as the
y-values of the function y =sinx. The graph for y = − sin x appears below:
1
1
2
zero
0
π
2
− 1 2
−1
minimum
zero
π
maximum
3π
2
zero
2π
Notice that, because of the negation of the y-values, the graph begins at 0, as does
the standard sine function, but the graph of y = − sin x first goes to a minimum
value before crossing through 0 again up to the maximum value.