Converting Inverse Trig Functions to Degrees

1. Oct 25, 2008

Liger20

1. The problem statement, all variables and given/known data
Hello, I have been doing some trigonometry lately, just trying to get the trig I need for calculus, and the book I am reading goes into inverse trig functions. The book dives into trig equations without giving a very good description of how to find the trig functions. I understand how to do stuff like cos^-1(2) in the calculator, and also how to flip the other reciprocal function, but this is where my understanding fizzles out: once you get the answer in the calculator, what operations do you perform on it? Because from what I understand, the answer you get in the calculator isn't the final answer. The answer to my question is probably very simple, but I would sincerely appreciate it if anyone could help me with this, because I'm itching to get through the trig and into calculus. Also, how much trig is required to sufficiently understand calculus?

2. Relevant equations

3. The attempt at a solution

2. Oct 25, 2008

HallsofIvy

Staff Emeritus
You can't do "cos^-1(2)" on a calculator or any other way- there is no such number!

What do you mean by "final answer"? Doesn't that depend on exactly what the question is? It is true that there are many angles, t, such that cos(t) is equal to a specific number (between -1 and 1), even if you restrict to 0 to 360 degrees and your calculator only gives you one answer. To find the others you have to remember basic properties of sine and cosine. I find it easiest to imagine a graph of y= cos(x), for example, with a horizontal line through it.

3. Oct 25, 2008

Liger20

D'oh, you're right, there is no such number. I was just trying to demonstrate a point. My problem in the simplest terms: I don't understand why I can plug an inverse trig function into my calculator, and then have it come out to be a number that the book says is wrong. What am I doing wrong?

4. Oct 25, 2008

HallsofIvy

Staff Emeritus

5. Oct 25, 2008

Liger20

No, it really is not the correct answer regardless of whether it's in degrees or radians.

6. Oct 26, 2008

HallsofIvy

Staff Emeritus

7. Oct 26, 2008

Liger20

Sorry, I really should have done that to begin with. Here are some of the problems that are confusing me:

Evaluate Cot^-1(-1)

In the degree mode of my calculator, I type tan^-1(1/-1) and get -45 degrees, but the book is telling me the answer is 135 degrees.

Evaluate arccsc(-square root of 2)

I type sin^-1(1/-square root of two) and get -45 when the book tells me 315 degrees (I realize that this is the same angle, so does either one work here)

It's mostly just the cotangant problem that has me worried, although there are other problems invloving the other trig functions and their inverses that this happens on.

8. Oct 26, 2008

HallsofIvy

Staff Emeritus
That is strange- unless there was more to the question than just "evaluate Cot-1(-1)". Cot(x)= cos(x)/sin(x) and that will be -1 when x= -45 degrees. It is also true that cot(135)= -1. Is it possible that you were asked to give an angle between 0 and 360 degrees? Obviously "-45 degrees" does not satisfy that.

Same point- is your book asking for an angle between 0 and 360 degrees?

It's mostly just the cotangant problem that has me worried, although there are other problems invloving the other trig functions and their inverses that this happens on.[/QUOTE]

9. Oct 26, 2008

Liger20

Actually no, nowhere does it specify any of those parameters that you suggested. I'm working out of the Trig for Dummies workbook. It's kind of a self study thing. If you don't know what is going on here, that's fine, I'm sure I'll be able to work it out eventually.

10. Oct 26, 2008

Liger20

Okay, actually I think I'm grasping how to convert them, now the problem is how I have to list answers beyond the first answer for the trig functions since they're all periodic. It gives me these two equations: x=30+360k or x=150+360k with no explanation of how these equations are used. For example, when it asks for me to list all the solutions of x=sin^-1(0), it lists x=180k, and I have no idea how they derived that answer. I know there's a logical relationship between all this, I'm just having a hard time grasping it.