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Expert: Sherry Wallin - 2/15/2010


Question
Hello Sherry

can you please help insolving 2 cosē Θ - 1 +cos Θ + 1 = 0: -360° ≤ Θ ≤360°

Answer
Freddie, simplify your equation
2 cosē Θ - 1 +cos Θ + 1 = 0 -> 2 cosē Θ +cos Θ  = 0 -> (cos Θ)(2cos Θ +1) = 0 ->cos Θ = 0 or
2cos Θ +1 = 0 so cos Θ = 0 at -3pi/2, -pi/2, pi/2,and 3pi/2. Now 2cos Θ +1 = 0 -> 2cos Θ = -1 ->
cos Θ = -1/2. The reference angle for cos Θ = -1/2 is in the 2nd and 3rd quadrant where x is negative is pi/3 so the answer is -2pi/3,-4pi/3, 2pi/3, and 4pi/3.

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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.

Education/Credentials
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.

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

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