You are here:

Advanced Math/Pre-Cal/Trig

Advertisement

Expert: - 3/9/2009


Question

Problems
Scott I'm having issue swith two problems in particular. I think, I always just loose my thinking in how to attack a problem. Well, can you help me with these problems?
1. Solve finding all solutions in [0, 2pie]?
cos2xsinx+sinx=0

2. Prove Each of the following identities?
Sec(4power)X-tan(squared)X = tan(4power)X+Sec(squared)X


Answer
By the way, pie tastes really good.  The term in math is the greek letter pi, which is 3.14159265358979... - doesn't taste that great, since I don't see any sugar in it anywhere ...

Now to look at the problems.

1. Factor out the sinx, giving sinx(cos2x+1)=0.

The solutions are sinx = 0 or cos2x=-1.

Remember the sin curve and solve the first one.

Remember the cos curve and solve the second one for 2x.
Once you have done this, divide the result by 2 to find x.


2. sec^4(x) - tan^2(x) = tan^4(x) + sec^2(x).

It is known that sinē(x) + cosē(x) = 1.
Divide this equation by cosē(x).
The result is tanē(x) + 1 = secē(x), or tanē(x) = secē(x) - 1.

Take both of the tanē(x) { since tanē(x)tanē(x) = tan4(x) } and
substitute this equation in and also put in the equation for secē(x).

The result is (secē(x)-1)ē + tanē(x) + 1.  Square the first term.
The result is sec^4(x) - 2secē(x) + 1 + tanē(x) + 1.

Rearrange the equation, giving sec^4(x) + tanē(x) + 2 - 2secē(x).

Now that 2 - 2secē(x) looks like 2(1 - secē(x)),
which is 2(-tanē(x)).

Putting this back in the equation gives
sec^4(x) + tanē(x) - 2tanē(x) = sec^4(x) - tanē(x).

Now if we look at that closely ... hey!
That's the value for which we are looking!  

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.