[AAHL][AIHL][AASL] Trigonometric equations

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Hello hello hello!

As you know we'll talk about trig equations after trig functions. 

After a short hiatus due to me unable to comprehend thermo, I'm now temporarily back with an ENTIRE (yes, entire) module on trig equations.

Have fun with it. Answers included at the end.


Link:



Where are we going, where have we been?

In our journey on trigonometry so far, we started with Pythagorean theorem and right-angled trigonometry. Extending our definition to larger angles, we develop the sine and cosine rules for non-right triangles and then to the entire unit circle. 

The "point on the circle" model gives rise to our trigonometric functions, namely, sine and cosine functions. We did a bunch of transformations to fit our function with our data, which is then used to predict future values.

The question arises: is there a way we could solve some equations without using a calculator? Answer: special trig values. More details on that soon.

Why are we interested in special trig values, I see you ask. We always want to try to minimise the possible error in each calculation. As we use the results from previous calculations to calculate more stuff, the errors get compounded and you'll end up with a LARGE error at the end. Recall that pi and many surds are irrational - the stuff you choose NOT to keep can fuck up the large calculation.


Credit: AdventurousAndrew#7499




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