Sine and cosine transforms Puns

3b1b's video was a great help in understanding Fourier transforms in the complex plane, but I was wondering there is some good material that would help me properly understand Fourier sine and cosine transforms. (This is for a college Calc-3 course)

I have a question about sine and cosine transform, and the question also includes a Heaviside function. I have tried to solve it but I think there is a problem with my solution. I suspect that it was caused by wrong integration of the Heaviside function.

Question: http://i.imgur.com/0R9kTtp.png My solution: http://i.imgur.com/gvCemN0.jpg

I would appreciate if anyone can help me on this question, thanks.

Later, I realized it was just a phase.

I need to make a program for my college course. It is for a grade. I don't know how to do a program for law of cosines or sines. The law of cosines one is more important, but he said it would be useful to have both. But the program is required for the class. I know how to use law of cosines, but he said we will need a program for the class. I already found a youtube video to show me how to do the quadratic formula, but I need the next two. Your help is greatly appreciated.

Hey everyone Yesterday i tried doing some trig and I got stuffed on when to use the sine and cosine rule (in particular the cosine rule). Can anyone give me an explanation as to how to apply both those formulas, in particularly the cosine rule?

Thanks everyone

Because together we would be one

My teacher was saying they were thinking of adding them but most questions ive seen seem really calculator based

I don't understand why can't we use cosine instead.

sin^2(x) = 1 - cos^2(x) is the same form has cos^2(x) = 1 - sin^2(x)

Is it because the derivative or integral of sin is ''easier'' than cosine because of the minus that we sometimes forgot?

Tank you

I know how SOH CAH TOA works but how does cosine of a number really result to a certain number? Is a number multiplied to that number? What is cos in and of itself?

Good day! I have watched the video of organic chem tutor about the subject (title) However i encountered a situation where its more than 360. when 0 <= x < 2pi, Find the value of sin 17pi /4

My intuition is to first convert it to degrees so its easier. converting it would result to 765 degrees so how should I do it? sin (360+405) but the rule is it should be less than 2pi / 360 degrees :/ .

I am still in grade school but I was curious about how the trig functions relate to rotation. I saw in a book that a Cartesian plane rotated at an angle θ's x' and y' coordinates can be written as x'=x cos θ
+y sin , y'= y cos–x sin θ. Also, I saw when programmers write code for a 3d engine the use sine and cosine for the rotation matrix.

I understand than sine, cosine and tangent are ratios of a right triangle and they can be used to find an angle or length of a side but I don't understand how it relates to rotation and how you can use them to rotate.

Please help, this may seem idiotic to ask especially considering my levels of math education but I've been at tit for a long time but I couldn't find it how it relates.

Hii, I need some help answering a question on sines and cosines. I am very familiar with these but the problem is that i learned these in my mothgerlanguage and not in english. So although im familiar with the concept, i don’t really understand the question because of language bariers. I hope someone can explain the question to me and tell me what theyre asking me to do.

I’ll explain for each part what I didn’t understand. the question i got:

Solve for α in the oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°

Oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°

1. Type out the two equations substituting the numbers from the diagram. (What do they mean with substituting numbers from the diagram? Do they want me to calculate the missing numbers on the triangle, as in BC and the angles from A and C?)
2. Type out the Law of Sines set of relationships and type out the most appropriate version to use the Law of Cosines for this solution. (Do they want me to calculate α (BC) using either of the two laws?)
3. Solve for a using both methods (show step by step work) ( I don’t understand what they mean here)

I hope my question was a bit clear!

So question, i know the formula to find period which is 2pi/b but im having trouble determining HOW i read this graph to figure out what im needing to do.

i understand i need to go from minimum to minimum then divide 2pi/? to figure out what my B is, but im genuinely lost on what to do when seeing this graph

I understand the amplitude is gonna be .5 as well as the vertical shift being .5

I see there's gonna be no phase shift

I understand this is COS

but like how do i read that and get pi?

The most i can get from this is MAYBE 3, but not pi which would give me 2pi/3

which is not 2, but 2.1

If anyone could point me to where im looking at this wrong or what i should try to do id be more than appreciative.

so id be .5 COS( ? X-0 )+.5

https://imgur.com/a/f8u1pXV

graph given for reference

https://preview.redd.it/e6qalm4t1pv71.png?width=395&format=png&auto=webp&s=e796c2bf51ee1f55c71e5184dbc4eb8f349a45eb

The top of a bucket 0.5 meters high is attached to a water wheel of diameter 2 meters, from which the bucket always hangs downward. The wheel sits above the river so that half of the bucket dips below the surface of the water at its lowest position. Write a function for the height of the center of the bucket (in meters) above the river as a function, f, of the angle t as measured counterclockwise from the 3 o'clock position.

h(t)= ?

Sorry for going on a tangent

I'm doing my math homework and typing Sine and Cosine functions into my TI-84 Plus, and depending on the number I enter, some of the results are in E notation. For example, if I entered 3cos((3/4)(3+(/4)) into my calculator, it would output: -3E -13, and I can't write that on my paper. If anyone has an explanation or if I'm doing something incorrectly, please let me know as I'm curious.

I just cannot for the life of me understand how sine, Cosine, and tangent work. I know how to get them but I dont understand what they mean.

Hi there people. I'm so sorry to ask you this trivial question, but I'm really racking myself trying to figure the process that matches the answer key. Here's the question:

sin(x) + sqrt(3)(cos(x))

Express the form as A sin (x + c).

Here's the hangups I'm having, if it'll help you understand where exactly I'm stuck:

So the amplitude of sin(x) is 1, the amplitude of this cos(x) is sqrt(3). In the answer key, the amplitude of the addition is 2, which is arrived by sqrt(3 + 1). Why is this so? I can't grasp the intuition.

I've tried converting the formula thusly (this is one of my attempts among many):

sin(x) + sqrt(3)sqrt(1-sin^2 (x))

sin(x) + sqrt(3-3sin^2 (x))

Now we have all sin values, but how do I get the right part out of the root? I've tried proceeding with multiplying by the conjugate of the root but it's not getting me anywhere.

Again, I'm sorry, but is there anyone who can identify this hangup and correct my procedure? I'm afraid I've worked myself into a box.

Edited to add answer: 2sin(x + pi/3)

Later on, I realized it was just a phase.

Because together we would be one

As I got older, I realized it was just a phase.