Answer to a Trig Question
Date: 1 May 1995 13:36:13 -0400 From: Jhone Ebert Subject: Help me Dr. Math! Hiya! Well, we have a little math question for you. What is the range of sin x = 1 / csc x ? This was a test question, in my Algebra II / Trigonometry class. My teacher marked it wrong when I answered All REAL numbers. She says that it is the answer is all real numbers except those that are integral multiples of pi. But my argument is right because 1 / lim x -> 0+ is 1 / infinite which is 0. Therefore all real numbers work. I am 15 and my friend is 15 and we both think we are right. What do you think? Thanks, James and Chonabot email@example.com
From: Dr. Sydney Subject: Re: Help me Dr. Math! Date: 3 May 1995 09:53:10 -0400 Hello again! It seems that I misunderstood your question the first time I read and answered it, so let me give it another shot. I thought you were asking what is the range of the function y = sin x (= 1/csc x), but some of the other math doctors have told me that when you ask what the range of an equation is, you are asking for what x values does the equation hold. So, to find the range of the equation sin x = 1/csc x we have to ask ourselves for what values of x does the equation work. I think your teacher has a point on this one, because csc x just is not defined for integral multiples of pi. You are right that 1/infinity is 0, and that is a good point, but I think the question is probably really asking at what values x are sin x and csc x nice... It is kind of like asking for what values the following equation holds (What is the range of this equation?) x^2 - 1 ------- = x + 1 x - 1 Think about this one, and see if you can figure out an answer and see why it is similar to your question. (It has a different twist to it, but see if you can figure it out! Write back with any more problems! --Sydney, "Dr. Math"
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