Question

What is The amplitude of f(x) = tan(1x) + 33?

Answer 1

Consider that tan a = (sin a)/(cos a), so that when "a" is close to, but still short of, 90 degrees, you are approaching positive infinity. Similar for "a" just over 90 degrees, you are approaching negative infinity. Therefore, the "3" is irrelvant and the amplitude is negative infinity to positive infinity.

Answer 2

ok is it okay if you can check if I got this right?
Find the equation of the cosine function with amplitude of 2/3 and period of 3pi and phase shift of-2pi and vertical shift of 1/3 units down

f(x) = 2/3 cos (2/3 x) - 1/3??

Answer 3

hold on, still checking.

Answer 4

ok

Answer 5

Everything is looking good except for the phase shift.

Answer 6

So its not 2/3x?

Answer 7

I think you are looking for f(x) = 2/3 cos (x + 2) - 1/3

Answer 8

That "x + 2" shifts everything 2 units to the left.

Answer 9

Okay, thanks for the help on the amplitudes :)

Answer 10

We're not done yet, though!

Answer 11

On the phase shift?

Answer 12

I just noticed that we have phase shift, vertical shift and amplitude all done now. But we still don't have a period of 3 pi yet.

Answer 13

oh ok I checked and the equation gave me 2pi

Answer 14

so we need to change the x+2?

Answer 15

y = (2/3) * cos ((x + 2)*(2/3)) - 1/3.

There, that's the final equation. You were good except for the phase shift.

Answer 16

Thanks for the help.

Answer 17

You're welcome!