Algebra and trig

This is a really big topic that is going to take many issues to develop. Here's the first bite sized chunk. We have a very simple formula that we start with.  Take these four equations and any introductory trig problem is solvable:

Algebra and trig

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This is a really big topic that is going to take many issues to develop. Here's the first bite sized chunk.

We have a very simple formula that we start with.  Take these four equations and any introductory trig problem is solvable:

• The angles of a triangle sum to 180
• The Law of Sines is sin(a)/A = sin(b)/B = sin(c)/C
• The Law of Cosines is A² + B² -2ABcos(c) = C²
• If you don't have a calculator, you can solve sins and cosines from the unit circle using the Pythagorean theorem (the reduced form of the Law of Cosines)

Then we attack problems.  It's simple to get started if you understand a bit of algebra.  Write down all of the equations and leave variables (like a or A) if you don't have a numeric value from the problem.  Any equation that has one variable is solvable, and you can chip away at the problem.

The fourth bullet above is going to require additional  sessions.  Sometimes we start with the fundamentals of the what and why of trigonometry, and sometimes little bits of this discussion sticks.  But in practice we iterate between what is trigonometry, why it is what it is, and how algebra applies.

I will present the fundamentals of trig in another bite sized chunk in a future article.

At this stage note that a and A are the angle and it's opposite side. We always relabel problems in this way and make c and C the biggest angle and longest side. Some day this won't be necessary. This approach to trig is designed for 10 to 12 year old children.