a Draw the point along the graphs of the sine and cosine functions.
B
b Draw the point along the graphs of the sine and cosine functions.
C
c Draw the point along the graphs of the sine and cosine functions.
A
a Cosine function, see solution.
B
b Cosine function, see solution.
C
c Sine function, see solution.
Practice makes perfect
a We are asked to determine whether we would use a sine function or a cosine function to model the described sinusoid. Let's start with the first description!
The y-intercept occurs at the maximum value of the function.
Let's graph this point and see whether we should use a sine or a cosine!
We notice that the cosine function is a better fit for the requested sinusoid. This is because the cosine function has its y-intercept at one of its maximums.
b Let's take a look at the next description.
The y-intercept occurs at the minimum value of the function.
Let's graph this point along the graphs of the sine and cosine functions!
We notice that none of the functions fit the description. Let's see what happens if we reflect the sine and cosine functions across the x-axis.
The cosine function is a better fit after the reflection. This is because functions of the form y=-cosx have their y-intercept at one of their minimums.
c Finally, we take a look at the last description.
The y-intercept occurs halfway between the maximum and minimum values of the function.
We will graph this last point along the graphs of the sine and cosine functions.
We notice that the sine function is a better fit for this situation. This is because the sine function has its y-intercept halfway between its maximum and minimum values.
