Question

Can someone help me on my Precalculus homework I'll attach a picture above...

Answer 1

Here's the pic of my homework, I don't know how to find the inverse of a function, also I don't know how to find the values of problems number 3-8, please help!!

Answer 2

It'd be less confusing for everyone if you'd post just one problem at a time. On which one would you like to focus right now?

Answer 3

On number 3 please!

Answer 4

First and foremost: the function y=arccos x is the inverse of the function y = cos x.

If you see "y=arccos x," think, "y is the angle that has cosine equal to x."
For example, arccos (1/2) is the angle that has cosine equal to 1/2, and that angle is 60 degrees. Check this on your calculator: cos 60 deg = 1/2.

Answer 5

Note: arccos (-1) could be re-written as arccos (-1/1). Since the cosine function is defined as cos theta = adjacent side / hypotenuse, the adjacent side here is -1 and the hypotenuse is 1. Could you draw that? Use the Draw feature, below, if possible.

Answer 6

how do you know that 1/2 is equal to 60 degrees?

Answer 7

You probably have either a calculator or a table of trig function values. If I were to ask you, "what is the sine of 30 degrees?" to where would you go for that information?

Answer 8

the unit circle?

Answer 9

There's something called a 30-60-90 (degree) triangle: From this triangle you can get the values of all six of the trig functions: sine, cosine, tangent, cotangent, secant and cosecant:

Answer 10

the unit circle should work fine also. But you still have to know the definitions of all 6 trig functions.

Answer 11

Hmm. So, if I were to use the unit circle for this the answer for number 3 would be 180°? Am I right?

Answer 12

Yes. I'd like to see how you got that: arccos (-1) = arccos (-1/1) => adj side is -1 and hypotenuse is 1, so we have an arrow of length 1 pointing from the center of our circle leftward tothe point (-1,0). Yes, the angle is 180 deg. Nice work! Note that 180 deg = pi radians.

Answer 13

I guided myself by seeing this unit circle. I found that 180° equals (-1,0) that it is equal to (cos, sin) so, the answer would be 180°... Am I ok? :D

Answer 14

It's great if you can successfully use the unit circle.

"I found that 180° equals (-1,0) that it is equal to (cos, sin) " unfortunately is inaccurate.

You could state that the adjacent side is the line segment from the origin (0,0) to the point (-1,0): It's -1. The radius of this circle is 1, so the hypotenuse is 1.

What are you trying to say with, "that it is equal to (cos,sin)"?

Answer 15

That the cos of 180° is -1 and the sine of it is 0 :o

Answer 16

You're quite right there. Please be careful not to write things such as "that it is equal to (cos,sin)" that lead to others' having to guess your meaning.

So: What's your final answer to this question? Is it possible that there could be more than one correct answer?

Answer 17

The answer is 180° but, since my teacher is asking me this on radians it would be pi!

Answer 18

that's right!

Answer 19

Thank you very much! :D Could you please help me on number 4?!

Answer 20

Please post #4 as a separate question, OK?

Answer 21

Ok! :D