Question

Okay I need help! My test is 2morrow. It's on Periodic functions and I don't understand how you can get the x-intercepts and y-intercept from an equation. Can someone please explain!!! Please. For example how would you find the first 3 x-intercepts and the y-intercept from the equation 1/3cos3(x-30)

Answer 1

1) You must learn to write clearly. Do you mean \(y = \dfrac{1}{3}\cos^{3}(x - 30º)\)?

Answer 2

oh sorry, one minute

Answer 3

2) x intercepts correspond to y = 0. Substitute and solve.
3) y intercepts correspond to x = 0. Substitute and solve.

Answer 4

oh okay. Thank you. Well the equation would be y=((1)/(3))cos(3(x-30°)) I still don't think I'm writing it right, but it's more clear, right? Sorry I just don't know how to use the site very well.

Answer 5

This is more clear. Good work. Parentheses help.

x-intercepts correspond to y = 0

0=((1)/(3))cos(3(x-30°))

0=cos(3(x-30°))

3(x-30º) = \(\dfrac{\pi}{2} + k\pi\) where k is an integer.

(x-30º) = \(\dfrac{\pi}{6} + k\dfrac{\pi}{3}\) where k is an integer.

x = \(\dfrac{\pi}{3} + k\dfrac{\pi}{3}\) where k is an integer.

That's all of them!

You do the y-intercept.