Advanced Math/math proof

Advertisement

Expert: Robi Bhattacharjee - 10/7/2008


Question

fig
How to prove Fx1 = FX1Cos Theta + FY1Sin Theta and Fy1 = -FX1Sin Theta + FY1Cos Theta?
The question is accompanied by two sketches of vectors labeled Fx1 and Fy1 respectively. In both cases the vectors are drawn on a XY scale and have two components FX1,FY1 and there is an angle theta between them. Note vectors are characterized by lower case letters and components are characterized by capital letters.

Answer
Hi Joe,

Sorry for the late response, I've had a lot of work. This statement is not true, so it cannot be proven. However, I think you might have confused this with some other statements.

Fx1 = Fx1Cos(theta) FX1 + Fx1Sin(theta) FY1.

This is because you simply have a right triangle, and an angle, so by elementry trigonometry, you can Show that the FX1 component is Fx1Cos(theta) and the FY1 component is Fx1Sin(theta).

As for your second question, I do not understand what theta has to do with the picture. Could you elaborate, theta doesn't connect to any of the vectors?

I hope this helped,

Robi  

Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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