Advanced Math/#3 Trig

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Expert: Sherry Wallin - 11/16/2009


Question

#3 Trig
I'm stuck and need some help.

Answer
Hi Jill~
    If P1 is on the wheel where it is shown and 2 seconds later P2 is at the top of the wheel then P1 is at 18 degrees or pi/10. A full circle is 2pi and the wheel turns 6 times in a minute so every 10 sec it make one turn so every one sec it makes 1/10 of a turn and 1/10 of 2pi is pi/5 or 36 degrees. When we are at point 1 the distance from the water is 6 feet and the radius is 7 feet so at P2 the maximum height is 13 feet. The height at P1 is 7sin(2t+1)pi/10 + 6 because the angle with the horizontal and the radius is pi/10 or 18 degrees. So d(t) = 7sin(2t+1)pi/10 + 6. To verify this take t = 0 and you get 7sinpi/10 + 6 = 8.163; t = 1 7sin3pi/10 + 6 = 11.663; at t = 3 7sinpi/2 + 6 =13. What you are doing is you are adding the 6 feet to the distance from the point on the circle to the water so it is always the side opposite the angle being made with the horizontal which is how the sine function is defined opp/hyp only now we want the height in y over the radius of the circle being your hypotneuse. When we get past pi the height will be subtracted from the 6ft. Try t = 5 for example. When t = 5 we have 7sin11pi/10 + 6 which is 7sin 198 deg + 6 = -2163 + 6 = 3.837ft. When the angle is 3pi/2 your height will be the smallest and the most negative. Remember we started at pi/10 at time zero so we need to add 14pi/10 to get to 3pi/2 so that means t = 7 let's check it out:
7sin(2(7)+1)pi/10 + 6 = 7 sin 15pi/10 + 6 = 7sin3pi/2 + 6 = 7(-1) + 6 = -1ft. The lowest point on the wheel is 1 foot under water!

Math Prof
    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentThanks for your help, I appreciate it.


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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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