Advanced Math/Trig Help

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Expert: Sherry Wallin - 1/15/2010


Question
How do I prove that -1 ≤ sinΘ ≤ 1 and that -1 ≤ cosΘ ≤ 1? I'm working with degrees, not radians, and I think I'm supposed to use trig identities (pythagorean identity) and/or the unit circle.

Answer
Here is one way of dealing with the problem. On the unit circle you can use the idea that
x = cos theta and y = sin theta. When theta = 0 then x = 1 which implies cos theta = 1. Square both sides getting cos^2 theta = 1 and now take the square root of both sides and you will get that
cos theta = +-1 (because you don't know whether theta is negative or positive and now this is true for all theta). Another way to write cos theta = +-1 is -1<= cos theta <=1. Sin theta is done similarly.

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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