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About Chen Min
Expertise
All the conceptual questions except for probabilities and statistics are welcomed. I am good at answering your algebra (including logarithm, functions, trigonometry) and geometry questions. I can also provide to you a firm understanding into calculus and other mathematical ideas and concepts. You can either ask questions in English or Chinese. Important:Please avoid asking me questions related to economics.After all, I am only a secondary school student

Experience
A lot of participation in Math Olympiad Competition with numerous awards (Not always gold, though)

Education/Credentials
So far, nothing.

You are here: Experts > Science > Mathematics > Advanced Math > Trignometry

Topic: Advanced Math

Expert: Chen Min
Date: 5/7/2008
Subject: Trignometry

Question
if sinx=3cosx, what is the value of sinxcosx.

Where do I start?

Answer
A very simple way is to get tan value of x;

tanx = sinx / cosx = 3

So, sinxcosx = 0.5 sin2x = 0.5* 2tanx / [1 + (tanx)^2]
            = 0.3

This is done by the first of the following identities:

sin2α=2tanα/[1+(tanα)^2]

cos2α=[1-(tanα)^2]/[1+(tanα)^2]

tan2α=2tanα/[1-(tanα)^2]

They are useful because they associate sin, cos, and tan values to tan alone, so as to manage and process them better.

An easier alternative is this:

As sinx = 3cosx
  sinx*cosx = 3(cosx)^2                   (1)
            = 3[1 - (sinx)^2]
            = 3[1 - 9(cosx)^2]
            = 3 - 27(cosx)^2              (2)
Hence from (1) and (2),
    30(cosx)^2 = 3
    sinxcosx = 30(cosx)^2 / 10 = 0.3
The key is to constantly substitute the unknown with the known.

Hope this helps:)

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