I don't know a lot of math, so I would love to learn about sine and cosine If you really know about math PLEASE teach me, thanks.

ok:
https://en.m.wikipedia.org/wiki/Sine_and_cosine

I didn't understand even 0.01% of what you just sent me

sine and cosine are complex subjects that involves learning many other math concepts for it to make sense. it's probably best that you learn these concepts in school so it makes sense when you learn it in your geometry class

or just take a khan academy course or something

Matruxo wrote:

I didn't understand even 0.01% of what you just sent me

its a wikipedia article

gdfsgdfsgdfg wrote:

Matruxo wrote:

I didn't understand even 0.01% of what you just sent me

its a wikipedia article

Wikipedia articles are not exactly known for being accessible for beginners, in terms of mathematical concepts.

Do you know what a right triangle is?

(I learned this last year so let's hope I can remember)

The main purpose of sine and cosine is to find unknown side lengths given some angle measure in degrees or radians (radians are a way to represent angles in terms of pi)

The outputs of sine and cosine usually fall on some spot on a unit circle, and can be used to form a triangle. The unit circle is split up into 4 quadrants like so:

2 | 1
——–
3 | 4

The output of sine gives the vertical length of the triangle and the output of cosine gives the horizontal length. For instance, the sine of 45 degrees and cosine of 45 degrees give 2√2, which should form a right triangle on the first quadrant

Sine and cosine (and tangent) can also be used to form repeating waves, which Scratchers use sometimes for cool effects

This is a right triangle. The red line is called the hypotenuse. It is opposite from the right angle (90 degrees).



In a simple explanation, sine, cosine, and tangent are each a ratio of sides in a right triangle.

A helpful name to remember each ratio is with the abbreviation, SOH CAH TOA. We'll go through each one.

———

SOH (Sine)

SOH stands for Sine = Opposite/Hypotenuse.

The opposite is the side across from the angle. For example, in the picture above, the opposite of angle C is line AB.

The hypotenuse is the side across from the right angle. For example, in the picture above, the hypotenuse of the triangle is line AC.

So, sin C = AB/AC
Substituting the values from the triangle,
sin C = 3/5

———

CAH (Cosine)

CAH stands for Cosine = Adjacent/Hypotenuse.

The adjacent is the side next to the angle, not including the hypotenuse (the hypotenuse is described as the hypotenuse). For example, the adjacent of angle C is line BC, because it is next to angle C.

The hypotenuse is the side across from the right angle. For example, in the picture above, the hypotenuse of the triangle is line AC.

So, sin C = BC/AC
Substituting the values from the triangle,
cos C = 4/5

———

TOA (Tangent)

TOA stands for Tangent = Opposite/Adjacent.

The opposite is the side across from the angle. For example, in the picture above, the opposite of angle C is line AB.

The adjacent is the side next to the angle, not including the hypotenuse (the hypotenuse is described as the hypotenuse). For example, the adjacent of angle C is line BC, because it is next to angle C.

So, tan C = AB/BC
Substituting the values from the triangle,
tan C = 3/4

———

So what can you do with these? Let's look at an example trig problem:


For this example, we will be trying to solve for side AC. Let AC be x.

We will use tan to find it and plug in what we know.

tan() = opposite / adjacent

Plug in the numbers from the problem
tan(35) = 8 / x

Multiplying both sides by x, we get
x tan(35) = 8

Dividing both sides by tan(35), we get
x = 8/tan(35)

Now, put 8/tan(35) in a calculator.
The answer is approx. 11.42518405

———

Hope this helps. Again, this not an extensive explanation and doesn't really show how to use it on Scratch.

Edit: corrected “SOH stands for Sine = Opposite/Adjacent.” to “SOH stands for Sine = Opposite/Hypotenuse.”

⬆️⬆️⬆️ leahcimto's explanation above is as good as it gets ⬆️⬆️⬆️
I do want to add a few things to it:

The functions are not only affiliated with right triangles, but circles too. In Scratch, we mainly use these functions for stuff related to circles and arcs.


Imagine you have a circle [with radius 1] and have picked a specific point in the circle.
You also have an angle ‘α’ which is the angle from 0° of the circle to your point.
Sine and cosine can be used to find the x and y position of your point in the circle.

In the image given above,
cos α would be the x position of the point
sin α would be the y position of the point

Let's say the radius is 1cm angle α is 30°.
That means the x position of the dot = cos 30° = around 0.866cm
and the y position of the dot = sin 30° = 0.5cm

If you have a circle whose radius is bigger than 1, then just multiply the radius with the result.
for example, if radius is 3, you can just do 3 × sin 30°

Remember that since Scratch's angles are 90° off, in Scratch, sin corresponds to x position and cos to y position.

Using all that, we can make a script to draw a circle using pen:

pen down
set [i v] to [0]
repeat (360)
set x to (([sin v] of (i)) * (radius::#666)) // In scratch, sin corresponds to x position
set y to (([cos v] of (i)) * (radius::#666)) // In scratch, cos corresponds to y position
change [i v] by (1)
end

In that script, we have a variable ‘i’ which we treat as the angle. The variable ‘i’ is iterated from 0 to 360, 360 being the number of degrees in a circle. To figure out where our sprite needs to go next while drawing the circle, we use sin to find out the x position, and cos to find out the y position. Then we multiply the result with the radius.

Probably the “easiest” explanation (depending on who you ask) is the following: below are graphs of sin(x) (red) and cos(x) (blue).

This doesn't actually explain what sine and cosine really are — see the two posts above mine for more detailed information — but at least it gives you a visualization of sine and cosine. For the purposes of using them on Scratch, this may be all that you need to know.

Here's an example project using that does what @Za-Chary is showing.

Draw a circle with radius 1 at the center of its plane and a line from the center outwards to infinity. Sin(x) is the height of the intersection from the center while Cos(x) is the width. X is the angle (defined by the originally drawn line and a line drawn from the center to directly right to infinity, it is the inside angle.) See image below.

See Source