Question

Find the exact value of this expression. Do NOT use a calculator.
cos^-1(0)
How do I do that without a calculator??

Answer 1

First a question: do you only know the definitions of sine, cosine, and tangent in terms of a right triangle or do you know it terms of a unit circle?

Answer 2

Right triangle...but if the unit circle hepls more with this question, i have notes i can look at.

Answer 3

Yup! So with the unit circle think of it this way. Cosine is really talking about the x coordinate of any point on the circle right?

Answer 4

yep.

Answer 5

so we basically give it the angle and we get the x-coordinate. Arc cosine or cos-1 is the reverse of that so we give it the x-coordinate and we get the angle out. So if we have an x-coordinate of 0 what would be our degrees on the unit circle.

Answer 6

Does that make sense?

Answer 7

yea i get it...would it be...-1?

Answer 8

-1 degrees?

Answer 9

wait...

Answer 10

sorry i was looking at the y corrd...90?

Answer 11

Yes! Exactly! Now another value you might have also thrown out there would be 270 degrees. But the arc cosine function range is only from 0 to 180 degrees (because otherwise it would not be a function)!

Answer 12

so the answer is as you said 90 degrees!

Answer 13

oh!! Wow!! Wait....So...even though its the inverse of Cos (cos^-1)...it doesn't matter, it still will equal 90? and still be in the same spot on the unit circle?

Answer 14

I don't quite get what you mean by "the inverse of Cos (cos^-1)"

Answer 15

Isn't \[\cos^{-1} \] the inverse of cos?

Answer 16

So if that's true, wouldn't it be different from cos itself? Wouldn't the answer be a negative number?

Answer 17

Yes arc cosine is the inverse of cosine. And yes it is different! But arc cosine cannot give you a negative number because it only gives you values from 0 to 180.

Answer 18

oh...lol duh...sorry, but thank you for answering my question!!

Answer 19

no problem and you're welcome!