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Calculus/simplifying

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Expert: Scotto - 7/1/2008


Question
how can this be simplified? sin(5lnx).

Answer
One way would be to say that sin(5ln(x))=sin(ln(x)^5).
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Another way would be to use the trig formula
sin(A+B)=sin(A)cos(B) + cos(A)sin(B)
with A=3L, B=2L (where L = ln(x)).

Use it again with A=2L, B=L on the terms with a 3L in them and note that cos(3L)=cos(2L)cos(L) - sin(2L)sin(L),
sin(3L)=sin(2L)cos(L)+sin(L)cos(2L).

Now use the formulas sin(2A)=2sin(A)cos(A) and cos(2A)=2cos^2(A)-1 to get rid of the terms with a 2A in them.

Combine all the terms together and note that all of them have a ln(x) in them as L.
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Then again, maybe we could ask what, 'What is the variable to which that equation is suppose to be simplified?'

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

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I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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