How do I find the arc cosine?

Question

I'm supposed to find the arc cosine of negative (square root of 3) over 2, and express it in radians.

okay, here you go, best I can using numbers: (sqrt3)/2, and the whole fraction is negative.

You don't have to answer the problem specifically, just explaining how I find the arc cosine, or the difference between the arc cosine and cosine would do.

Answer 1

Arc trig functions can be tricky, but they don't have to be. The fastest way to compute this answer is to lay out the table on regular trig:

Degrees: Formula: Simplification: Radian Notation

SIN:

0 degrees = (sqrt 0) / 2 = 0

30 degrees = (sqrt 1) /2 = 1/2 = pi/6

45 degrees = (sqrt 2) / 2 = pi/4

60 degrees = (sqrt 3) / 2 = pi/3

90 degrees = (sqrt 4) / 2 = 1 = pi/2

COS:

0 degrees = (sqrt 4) / 2 = 1

30 degrees = (sqrt 3) /2 = pi/6

45 degrees = (sqrt 2) / 2 = pi/4

60 degrees = (sqrt 1) / 2 = 1/2 = pi/3

90 degrees = (sqrt 0) / 2 = 0 = pi/2


TAN = (sin/cos)

0 degrees = 0

30 degrees = 1 / srt 3

45 degrees = 1

60 degrees = sqrt 3

90 degrees = undefined


In your problem, the sqrt of 3 over 2 corresponds to 30 degrees, which is expressed as (pi/6) in radians. The negative, I believe (in this case) has no impact.

Sorry about the format - yahoo's restrictions are terrible. Hope this helps!

To answer your question, arc cosine is the reverse of the function.

For example:

cosine (30) = sqrt 3 / 2

arc cos (sqrt 3 / 2) = 30

Answer 2

It would be better if you'd use more standard notation, i.e. -sqrt(3)/2 or -(3^1/2)/2. Math is hard enough without trying to write equations in words.