Converting Inverse Trig Functions to Degrees

[Liger20]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Homework Statement

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

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

, 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.

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.

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?

Homework Equations

The Attempt at a Solution

 

[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?

 

[HallsofIvy]

First, is your calculator in "degree" or "radian" mode? Second, is the answer in the book in degrees or radians?

 

[Liger20]

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

 

[HallsofIvy]

Then please tell us what the problem is, what answer your calculator gives and what answer your book gives.

 

[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.

 

[HallsofIvy]

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.

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.

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)

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]

 

[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.

 

[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.