Current Events > Is there anyone who is good at sine and cosine stuff

(+) Yeah! (+)

I am sucking ass at this -_- Have a circle centered at 0,0, radius of 8 units, a point in the third quadrant of -7.1,-3.5 , and the angle I calculated was 205 (about 3.57 radians).

I need to evaluate the sine and cosine of this angle and I'm just lost af, have read the text book, watched videos, tried just playing around with numbers and nothing is adding up -_-. If I understand correctly, the two resulting measurements should somehow be able to add up/square up to the square of 8, but I can't.

Also had to do this by hand so my measurements are probably off fml

---

The sine function fluctuates between -1 and 1. The cosine function also fluctuates between -1 and 1.

There is no way that they would add up to the square of 8. Their sum must be between -2 and 2

xue1 posted...

The sine function fluctuates between -1 and 1. The cosine function also fluctuates between -1 and 1.

There is no way that they would add up to the square of 8. Their sum must be between -2 and 2

Hmmmmm

So in this context what is "-1" and "1"?

Trying how to formulate the question right... is it the radiant angle from the point of origin?

I just got confused because I saw one video where they say "sine = the y value of a point on the circumference and cosine = the x value of that point", Don't know if that's too accurate - in the third quadrant my points are both negative values and I end up with .68 and .35 for the x and y respectively if I plug the coordinates from OP in.

---

I got ~-153.758667 degrees which is about what you got.

---

1337toothbrush posted...

I got ~-153.758667 degrees which is about what you got.

Lmao I'm ... fucking stupid. How is that about what I got >_>

---

360 degrees - 153.758667 = 206.241333 but my calculation likely has rounding errors.

---

1337toothbrush posted...

360 degrees - 153.758667 = 206.241333 but my calculation likely has rounding errors.

So where did the 153 come from >_>

I also have to double check my math, I am not 100% certain if it was 205 or 195 now.

---

Bump. Still not sure how to formulate / graph this stuff out.

---

This is why i stopped math at geometry in high school. Fuck this shit lol

x = r*cos(theta) => cos(theta) = x/r
y = r*sin*(theta) => sin(theta) = y/r


---

It was mandatory I learn all this crap in HS and I have not, and will not use it in my entire life, and also couldn't do it to save my life if i needed to

---

(Rsinx)^2 + (Rcosx)^2 = R

x = atan(-3.1/-7.1) + 180 = 206.25

8sin(206.25) = -3.53
8cos(206.25) = -7.17 (close enough I guess)

(-3.53)^2 + (-7.17)^2 = 63.9

8^2 = 64 ~ 63.9

---

As for graphing, just plot (8,0) (-8,0) (0,8) and (0,-8) and draw a circle between the points. For more precision, feel free to find points at 45 degrees counter clock wise of those four points where the coordinates are

(Rcosx, Rsinx), and X is your angle.

---

sinx = 3.5 / h
h = sqrt((-3.5)^2 + (-7.1)^2)

-> x = sin^-1(3.5 / h)
Total angle is x + 180.

I get about 206 degrees.

---

Conceptually, the coordinates of a circle, at any angle, are the radius multiplied by the cosine and sine of the angle you're interested in. If it's a convenient way to find information on a circle.

It is also a convenient way to break down a vector into its X and Y components.

---

Thank you everyone for posting your solutions and the explanations, it helps a ton and I will be going through it in a few hours to make sure I understand, especially @Jabodie but I also appreciate your answer @EmbraceOfDeath and @Shadow_Don .

For some reason it's just not conceptually clicking, even though it actually looks really straightforward and it is driving me crazy. But I will play around with these numbers again tonight.

ThePhantomMedic posted...

This is why i stopped math at geometry in high school. Fuck this shit lol

Despised posted...

It was mandatory I learn all this crap in HS and I have not, and will not use it in my entire life, and also couldn't do it to save my life if i needed to

Yeah I got to Algebra 2 in high school so... I never even learned this stuff (or at least definitely don't remember it lmao I failed math hard). Was doing fine in the previous two classes on functions but I'm having a hard time contending with the material and structure of this one.

---

Whoops that first formula should be

(Rsinx)^2 + (Rcosx)^2 = R^2

Feel free to tag me for questions later

---

Hexenherz posted...

For some reason it's just not conceptually clicking, even though it actually looks really straightforward and it is driving me crazy. But I will play around with these numbers again tonight.

That's normal. Math is really hard and it takes a long time to learn. One problem I see that most people have is that as soon as they get stuck they think it's because they are stupid and want to give up.

I struggled with trigonometry too when I first saw it but I ended up with a graduate degree in math.

I like to think of the x-axis as being the cosine-axis and the y-axis as being the sine-axis.

If you have the radius and (x,y) coordinates you can calculate cos(theta) and sin(theta) without knowledge of what theta even is with the formulas I posted above. If your problem was simply to find what cos(theta) and sin(theta) are then that's all you need.

On the other had if you have the radius and theta then you can calculate the (x,y) coordinates.

It seems pointless and stupid but for engineering and physics the trig functions are extremely important. Like every single page in a quantum mechanics textbook will have trig functions on it.

---

What drove you to pursue mathematics? It is interesting and I like learning the logic of things but for some reaaason... maybe I should join the study discord they set up for the class

---

This is actually killing me...

So I remeasured the angle and using 206 degrees I can get 64 *on the dot*, but this also means my physical measurement using a string, and my original coordinate points probably aren't correct. In other words all these figures throw off my previous work -_-.

Now, this was all originally drawn up by hand with rulers and everything so I imagine there's some tolerable margin of error... or at least I'm hoping so -_-. Or maybe I just include that in my assignment's write-up.

---

I took a picture of my circle to include with my assignment and the file size is 3.14 MB wtf.

---

Nice topic

---

Just want to say thanks again to everyone who helped, between your assistance and spending many many hours trying to figure it out I was finally able to make sense of it and it was much easier than I expected lol.

Now on to graphing sinusoidal functions -_-

---

Hexenherz posted...

If I understand correctly, the two resulting measurements should somehow be able to add up/square up to the square of 8,

No, you're mixing up two separate concepts here

Pythagoras' theorem states that the square of the hypotenuse is equal to the square of the opposite plus the square of the adjacent. You may know it as a^2 + b^2 = c^2

With your angle and your given point (which I'm assuming is on the circumference) you can construct a triangle which will fulfill Pythagoras, and use the sine and cosine to help you do so. But the sine and cosine themselves won't add up to 8^2
---

Feel free to tag me in any future math topics TC. I was a tutor in undergrad so I get a kick out of this.

---

I was really good at it in college. Now I have to stop and think about how to push it in the calculator. :(

---

teep_ posted...

No, you're mixing up two separate concepts here

Pythagoras' theorem states that the square of the hypotenuse is equal to the square of the opposite plus the square of the adjacent. You may know it as a^2 + b^2 = c^2

With your angle and your given point (which I'm assuming is on the circumference) you can construct a triangle which will fulfill Pythagoras, and use the sine and cosine to help you do so. But the sine and cosine themselves won't add up to 8^2

Thanks lol. The way I came to understand it now, for circles at least, is that sin = y distance up or down from the x-axis to the point on the circumference (I was measuring it in radians) and cosin = x distance left or right from the y-axis to the point on the circumference, and it ends up basically being a percentage of the radius (from 0 to 100%) and... yeah. Probably somehow entirely conceptually wrong but I have been getting correct answers with this logic so maybe there's something to it.

@Jabodie Thanks lol, I know how it feels to know something and be able to help others and it is a good feeling. Appreciate that you put a lot of time into helping here.

Just built my first sinusoidal function and it actually lined up exactly with the sample graph we were supposed to emulate, so that feels good.

I am nervous as shit that I am just learning shortcuts or something instead of the full theory behind all these things and that will come back to bite me in the ass though.

---

Hexenherz posted...

The way I came to understand it now, for circles at least, is that sin = y distance up or down from the x-axis to the point on the circumference (I was measuring it in radians) and cosin = x distance left or right from the y-axis to the point on the circumference, and it ends up basically being a percentage of the radius (from 0 to 100%) and... yeah

Yup, as long as you keep in mind that it's the co-/sine of the 'angle in the middle of the circle'

And no, it's not conceptually wrong. It's pretty much how you define the sine of an angle (or one of the ways anyway)
---

xue1 posted...

The sine function fluctuates between -1 and 1. The cosine function also fluctuates between -1 and 1.

There is no way that they would add up to the square of 8. Their sum must be between -2 and 2

The sine and cosine probably have a coefficient out front. So TC is probably looking for something of the form:
a*sin^2(x) + b*cos^2(x) = r^2

---

Hexenherz posted...

and it ends up basically being a percentage of the radius (from 0 to 100%) and... yeah.

To flesh that out a bit:

cosine and sine describe a circle with a radius of 1. So for any angle theta,

cos(theta)^2 + sine(theta)^2 = 1^2 = 1

Now, if your radius is not 1, you multiply that equation by your radius squared, R^2:

R^2*cos(theta)^2 + R^2*sin(theta)^2 = R^2

[R*cos(theta)]^2 + [R*sin(theta)]^2 = R^2

That is to say: it is the square of cosine and sine that add up to 100% of the radius squared.

It also means that at any angle on the circle, the x and y components are

x = R*cos(theta), y = R*sin(theta) (what you said, more or less), but the magnitude of these will not add up to R (unless one of them is zero).

Additional considerations: If you have the origin and a single point on a circle, you can find the radius of the circle and every other point on the circle using the equations above.

If instead, you have the origin and the radius, you can find every other point on the circle using the sinusoidal functions as well.

Edit: Also, sine and cosines are used to describe waves, or pretty much anything that is cyclic. But that's another topic.

---

Lol it's about to be this topic because that's what we're getting into right now. It helps being introduced to the graph as a visualization tool, too, since I can see what this all amounts to.

Also actually was able to use this to help with a different class I am taking right now so that felt good.

---

Like, with absolutely zero context how are you supposed to tell if something is a sine or cosine function? Or is it just safe to assume that if the y-axis doesn't intersect the middle line at x = 0 then it's just a cosine? -_-

---

Graphically? Not necessarily.

cos(x) = sin(x+90) or sin(x + pi/2) (double check me here)

With these functions you can model them with either. Usually you want to choose whatever is more convenient for whatever you are doing.

---

Hexenherz posted...

I took a picture of my circle to include with my assignment and the file size is 3.14 MB wtf.

Lol thats awesome!

---

My mind always says sin = y direction
cosine = x direction

when thinking about unit circle

---

Hexenherz posted...

Like, with absolutely zero context how are you supposed to tell if something is a sine or cosine function? Or is it just safe to assume that if the y-axis doesn't intersect the middle line at x = 0 then it's just a cosine? -_-

Cosine is just a sine function with an offset.

---

Hexenherz posted...

Like, with absolutely zero context how are you supposed to tell if something is a sine or cosine function? Or is it just safe to assume that if the y-axis doesn't intersect the middle line at x = 0 then it's just a cosine? -_-

at x = 0, if y is 0 then it's a sine

at x = 0, if y is at its largest (or smallest) value then it's a cosine
---

This is all about the Unit Circle. I suggest looking up some YouTube tutorials on it. Unit Circle looks really complicated at first, but honestly it is really easy.

---