Question

Write the equation of the function represented by the following graph.

http://prntscr.com/b8vej0

I got y=3 sin (3x-{pi/2})

I just don't really know how I got the pi/2 for the horizontal shift...

Answer 1

I'm trying to start from the beginning ignoring what you did.

Do we have to use sin or can we use cos? :P

Because:

sin x = cos (90 - x)
cos x = sin(90 - x)

Answer 2

I'm not sure lol

Answer 3

I think I just learned sin and tan x'D

Answer 4

Because the graphs of sin and cos are just each other but just shifted. For this, it would be easier to use cos.

You got the -3 part in the beginning correct since the amplitude is 3, and it starts from the bottom

Answer 5

Okay

Answer 6

Now if we look at the graph in your question, we see that one period is completed at pi/2

And normally cos (or even sin for that matter) have a period of 2pi

so if

cos x has a period of 2pi

By how much do we have to divide 2pi to make it pi/2?

Answer 7

4?

Answer 8

So

cos x has a period of 2pi

cos 4x has a period of pi/2

So now we have

y = -3 cos(4x)

And we're all done :)

Answer 9

Awesome, thank you

Answer 10

It was my pleasure!

Answer 11

Remember

\(cos(\beta x) \) has a period of \(\Large \frac{2\pi}{\beta}\)

Answer 12

Okay, thank you soooo much!!

Answer 13

same goes for sin

tan and cot are the only ones that have a period of \(\pi\)

and so

tan(\(\beta\)x) has a period of \(\Large\frac{\pi}{\beta}\)

Answer 14

It was my pleasure!

Answer 15

I have notes on tan and sin, but not cos XD