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Expert: Sherry Wallin - 7/29/2010


Question
Given that sinα = 4/5, 0 <α<π/2 and sinβ = 5/13, π/2<β<π find the exact value of cos(α+β)

Answer
Kevin~

Since the sina is 4/5 and in the first quadrant that means cosa will be positive and using right triangle geometry you know that the hypotenuse is 5 and the vertical leg is 4 so
x^2 + 4^2 = 5^2 -> x^2 = 9 -> x = 3 -> cosa = 3/5
Now B is in the 2nd quadrant so the right triangle bears x^2 + 5^2 = 13^2 -> x^2 = 12^2-> x = 12 but again we are in the 2nd quadrant so that means x = -12

using the formula for the sum of cosines:
cos(a + B) = cosa cosB - sina sin B -> (3/5)(-12/13) - (4/5)(5/13) = -36/65 - 20/65 = -56/65

Thus the cos(a+B) = -56/65

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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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