Is someone here willing to help me with trigonometry

Yeah ig but khan academy only has like 4 questions and then your done. I think I will watch the videos in khan academy and then do the practice in IXL. Also, the IXL which I have is free because my 5th grade teacher (im in 6th grade) forgot to cancel the membership after the school year so I still have it.

some of the excerices have 7 though

that still isn't enough tho

ig, but they still have videos for you to actually understand

Oh, I forgot one of the first applications you learn.

So in your first physics class you usually use it for stuff like a box on a ramp. (You can literally google "box on a ramp problem" and find pictures like the one below).

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So look at the angle theta which is shown on the triangle with this symbol θ

Notice the dashed line is going through the center of the box. So θ is essentially showing you how tilted the box is. If θ is zero then it's just on flat ground, a completely horizontal surface. If θ is 90 degrees then it's on the side of a wall, a completely vertical surface.

Ok that was a long setup, but now the application. Now look at:

Fg Cos(θ)

Fg is just the force of gravity and Cos(θ) is going to give some number between 0 and 1. What it represents is the percentage of the force caused by gravity that is pressing the box against the surface. On a vertical wall θ is 90 degrees. and so Cos(θ) is zero. It means gravity isn't pressing the box against the wall... well of course! That makes sense to us.

If θ is zero degrees then the box is on a completely horizontal floor. Cos(θ) is 1. So 100% of the box's weight is pressed against the floor, that also makes sense to us.

But when θ is some angle like 45 degrees, some fraction of gravity's force is pressing the box to the ramp's surface and some fraction of gravity's force is pushing it down the ramp.

FgCos(θ) is pressing against the surface and FgSin(θ) is making is slide down the ramp.

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Ok, a bit more practical than a box on a ramp is hanging a sign.

Let's say you attach a cable to help hold the sign as shown below

But you need to know how much force is trying to pull the cable out of the wall. The horizontal force is calculated by taking whatever force the sign is causing due to gravity, then multiplying by Cos(θ)

So again, let's check if that makes sense.

If θ is 90 degrees, then Cos(θ) is zero. Well of course none of the force is pulling on the cable horizontally in that case (the cable would be attached directly overhead, to a ceiling. All the force would be vertical). Ok, so that makes sense.

If θ is zero degrees then all of the force is trying to pull it out of the wall horizontally. None of it would be pulling down. That also makes sense.

Yeah, exactly. Theta is a variable.

Just like in algebra X is some number. Sometimes you're solving for X, but other times it's a placeholder and you can plug in whatever number you want for X. In this case we can plug in any angle for theta.

So in a real problem you'd be given the value. For example "Find the force making the 10 kilogram box go down the ramp if it's inclined at 20 degrees"

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I didn't realize you're 12. You're asking good questions  Sorry if it's a bit confusing.

A better intro to applying trig is like the first thing I said. Holding a long measuring stick in a dark room. Put the flashlight at one end and put the stick at the other end of the room.

At first hold the stick flat against the wall, and of course the shadow will be just as tall as the stick... but if you pull it away from the wall so that there's an angle... (see picture below)

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Then the shadow is not as tall.

If the angle is 45 degrees, and the stick is 1 meter long then the shadow will be...

About 0.7071 meters tall. Why that number? Because cos of 45 degrees in decimal form is roughly 0.7071

And what if you lie the stick flat on the ground? In that case theta is 90 degrees and there's no shadow... because cos of 90 degrees is zero!

Thanks for the explanation, it makes sense now

The top. The angle it makes with the wall.

So if you pull it 30 degrees away from the wall the shadow should be about 0.866 meters high (if the stick is 1 meter in length).

Cosine is adjacent over hypotenuse. In this case the shadow is adjacent and the stick is the hypotenuse.

So you're right, to find the adjacent you'd have to multiply Cos(30) by the hypotenuse.

(adjacent / hypotenuse) * hypotenuse = adjacent

But in this particular case I made the stick 1 meter, so we'd just multiply by 1.

Let's say its an 8 meter stick 60 degrees away from the wall. Cos(60) is 1/2 so the shadow is (8)*(1/2) = 4 meters tall.

dang im smart for my age but not that smart I only got like half of what you said xD

Yes, good job

lol i take math very seriously tho and i do like at least 1 hour a day idk if its worth it xD

Here's an interesting question, let's say you do two flashlights, and so you have one shadow on the wall (Cos) and one shadow on the floor (Sin)

Will the length of those two shadows add up to the length of the stick? Or will they add up to something longer or shorter?

only 1 hour?

I'd give myself an A+ for that answer.

Anything else is less elegant.

This is the sort of math most people learn in high school. For some people (depending on their major) not even until they enter college.

So that's very impressive for a 12 year old.

There is a place for understanding trigonometric relationships, but it is not for real problem solving. It's not for the average person. It's for specialist mathematicians who wants to understand the algebraic relationships.

Sure, whatever answer helps someone understand is a good answer.

I agree math is taught poorly. I would introduce real physical examples (such as with shadows) that make it seem real instead of just arbitrary rules you're forced to memorize. "The value of the X coordinate is your Cos" well ok, but as a kid that'd just make me believe the teacher doesn't actually understand and is just reading the book. When I was a kid sometimes I'd go home and spend a few hours thinking about what a rule actually means... which is what this kid seems to be doing, which IMO is excellent.