Purpose of general soluion

your teacher is trying (and apparently failing) to teach you to think about things symbolically/algebraically instead of just typing numbers into your calculator

>>285983
No I finished school but I didn't do so well in maths so I became a carpenter but im doing a maths correspondence course

I understand what to do to solve(using ref. angle, changing subject of formula etc.) and the only thing you really need a calculator for is the reference angle, but I want to know where it is applied in reality! I'm bad with theoretical things and its easier if I can imagine a problem in a practical scenario

pls help

>>285993
Well I could help you more if you posted an example of the kind of problem you're struggling with.

If you have the "general solution" for a problem then you can easily get specific solutions no matter what the numbers involved are, whereas if you only work out a specific solution then you'll have to re-do it and calculate everything again if any of the measurements change.

>>286001
No its fine I think you've inadvertently answered my question to a certain extent

> "you can easily get specific solutions no matter what the numbers involved are"

So basically we can use a general solution for anything with a set pattern, like a number pattern then?

but then, what about an ambiguous solution? does that mean for example that one value in a no. pattern will hold to positions in the pattern or something?

>>286001
I'm not struggling with any problem in particular but I am finding it hard to wrap my head around the concept of solving for a general solution- why am I doing what I'm doing?

Correspondence courses have no physical lecturer and my textbook is only telling me the basics. I can do standard sums but this means nothing if I can't comprehend the purpose of the steps involved- I'd just be a zombie that gets stuck when something "hard shows up", you know?

File: Capture.png (13KB, 1055x661px) Image search: [Google]

13KB, 1055x661px

>>286035
The point of a general solution is that you can use algebra to get the answer for every similar situation. If you derive an equation with a variable in the solution, then you should be able to answer that question in multiple contexts, by plugging in the variable. Here's an example. You have a circle b with circumference c. What's the length of a 90 degree arc of circle b?

The length is c/4. So if you're given any circle of any size, you can find the length of the 90 degree arc just by knowing its circumference, and putting that in the equation.

The ambiguous solution is a case where you don't have enough information to find a definitive answer. Trigonometry requires you to have a minimum threshold of information to find a specific triangle.

For instance, if you know the lengths of all three sides of a triangle, you know exactly what triangle it refers to, because 3 sides is enough to determine both the sides and the angles. However, if you are given ONLY the three angles, you don't know exactly what triangle is being referenced, because the sides can be scaled up or scaled down. If you are given all three angles and the length of a specific side, you can determine the exact triangle.

Here's an example of an ambiguous question. You know an angle, and the lengths of two sides. But it could refer to either of the two triangles because you aren't given enough information to distinguish them.