Question

arccos(-1)

Answer 1

PLEASE HELP

Answer 2

Remember the unit circle with the trig functions? We are trying to find the angle \(\theta\) such that \(\cos(\theta) = -1\). At \(\theta = 0\) what does \(\cos(\theta)\) equal?

Answer 3

-1?

Answer 4

Nope.

Answer 5

Remember that the circle is \(2\pi\) radians around. At \(\theta = 0, \cos(\theta) = 1\) and \(\sin(\theta\) = 0\). What would the angle have to be to get \(\cos(\theta) = -1\)?

Answer 6

it says to give your answer using the form A(pi symbol)/B

Answer 7

Okay, we're just trying to find one value first, then we'll figure out the pattern.

Answer 8

0

Answer 9

No, cos (0) = 1. It goes from 0 to x in my diagram, and at a = 0, point x is at (1,0). For cos (angle) = -1, the radius has to be pointing into the left half of the circle.

Answer 10

oh okay makes sense

Answer 11

So, the axes cross the unit circle at \(\theta = 0, \pi/2, \pi, 3\pi/2\). At \(2\pi\) we've come full circle. Which of those values gives us \(\cos(\theta) = -1\)?

Answer 12

pi

Answer 13

Right! Now we just to figure out the pattern, because if we add \(2\pi\) to that, we also get the same answer, right? Or if we subtract \(2\pi\).

Answer 14

correct

Answer 15

Sorry, I didn't see that you'd responded. So our valid answers to \(\cos(\theta) = -1\) are \(\theta = \pm \pi, \pm3\pi, \pm5\pi, ...\) or \(\theta = \pi+2\pi{n}\) where \(n\) is an integer. I think your problem asking for an answer of the form \(A\pi/B\) is just so you didn't answer with 3.1415926535....our values for A and B are both 1.