Question Video: Finding the Maximum Value of a given Sine Function Mathematics

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.