Video Transcript
Find the maximum value of the
function 𝑓 of 𝜃 is equal to 11 sin 𝜃.
Firstly, we’re going to recall what
the graph of 𝑓 of 𝜃 equals sin of 𝜃 looks like. It has maxima and minima at one and
negative one, respectively. We know that it passes through the
origin and that it’s periodic and it has a period that repeats every 360
degrees. So, 𝑓 of 𝜃 equals sin of 𝜃 has a
graph that looks a little something like this. But of course, we were actually
interested in the graph of the function 𝑓 of 𝜃 is 11 sin 𝜃.
And so, we recall that for a
function 𝑦 equals 𝑓 of 𝑥, 𝑦 equals 𝑎 times 𝑓 of 𝑥 represents a vertical
stretch by a scale factor of 𝑎. In this case, we can see our scale
factor is 11. And so, 𝑓 of 𝜃 equals 11 sin 𝜃
looks something like this. It still intersects the 𝑥- and
𝑦-axes at the same places, but now it travels as high as 11 and as low as negative
11. And so, the maximum value of the
function 𝑓 of 𝜃 equals 11 sin 𝜃 is 11.
