Be careful! In this context, tangent refers to a line that touches a graph at one point. It does not refer to the trigonometric function!
Graph:
Conclusion: See solution.
Practice makes perfect
Consider the given graph.
We are told that the slope of the shown tangent line is m=1. Let's estimate the slope of other points of the graph!
We can see that the slope of the tangent line is 0 at the maximums and the minimums of the graph. Next, we will compare the slope of the line at x=-2Ď€ and x=2Ď€ with the given line.
Let's now focus on the points at x=-Ď€ and x=Ď€.
The lines at these points appear to have the same slope as the given line, but with negative sign. Let's summarize our findings in a table!
x
Slope of the Tangent Line
-2Ď€
1
-3Ď€/2
0
-Ď€
-1
-Ď€/2
0
0
1
Ď€/2
0
Ď€
-1
3Ď€/2
0
2Ď€
1
Finally, we will graph these points in the same coordinate plane. We can see how the points fit in the graph of a cosine function!
If we graph the slope of a line tangent to the sine curve at each point, we get the graph of a cosine function.
