Question

Compare and contrast Sin and Cos functions.
Hint: Period, shape, minimum point, maximum point

Answer 1

Do you mean \(\mbox{sin x}\) and \(\mbox{cos x}\)?

Answer 2

@tinybookworm the functions so I guess, yeah

Answer 3

The period of both \(\mbox{sin x}\) and \(\mbox{cos x}\) is \(2\pi\).

Answer 4

I have that.

Answer 5

Next, you may already know how they look like, the sinusoid

Answer 6

@marshallinwashington can you help?

Answer 7

@tinybookworm What is the sinusoid again?

Answer 8

It is the sine wave form, like this

Answer 9

Thanks. Anymore?

Answer 10

And the max and min points:

In the function \(\mbox{y = sin x}\), the max points are \(\large (\frac{\pi}{2},1)\), \(\large (\frac{5\pi}{2},1)\), \(\large (\frac{9\pi}{2},1)\), \(\large (\frac{13\pi}{2},1)\), and so on. The min points are \(\large (\frac{3\pi}{2},-1)\), \(\large (\frac{7\pi}{2},-1)\), \(\large (\frac{11\pi}{2},-1)\), \(\large (\frac{15\pi}{2},-1)\), and so on.

In the function \(\mbox{y = cos x}\), the max points are \((0,1)\), \(\large (2\pi,1)\), \(\large (4\pi,1)\), \(\large (6\pi,1)\), and so on. The min points are \((\pi,-1)\), \(\large (3\pi,-1)\), \(\large (5\pi,-1)\), \(\large (7\pi,-1)\), and so on.

Answer 11

As you can see in the picture, the wave is repeated so there are infinite max points and min points

Answer 12

Thank you

Answer 13

You are welcome