# sin

1. ### sin(x) as a vector

Hi! I could do with some help on an assignment for my calculus class! This is the info given at the beginning of the assignment: Fourier series can be seen as a generalisation of the idea of the scalar product. Consider on the one hand the ordinary vectors v1 = (1, 1) and v2 = (1,°1), and on...
2. ### Hi, I have tried to work out the following...

...can someone help me. Sine cosine tangent angles i have attached the following thanks in advance!
3. ### Integral of sin x cos2 x sin(cos x) dx

I need to calculate the integral of sin(x)cos2(x)sin(cos(x)) dx (without specific boundaries) but I'm struggling with this one. Can someone help me?
4. ### Integral of (cosx+sinx)^2dx

I did this but not sure if it is correct: ∫(cosx+sinx)^2dx= ∫(cos^2x+2cosxsinx+sin^2x)= ∫(2cosxsinx)= 2∫cosxsinx= 2sinx-cosx+C <--------End
5. ### Developing a double angle formula for Sin4x

Hi, I hope someone can help. I'm just trying to understand how Sin4x can be placed into a double-angle formula. One of the ways that I came across is as follows: Can someone please tell me the thought-process behind the first-step? I know that 2Sinx= 2SinxCosx, but where does the (2) and...
6. ### Find solutions for SIN(x)=-a, where a=SIN(α) for 0<α<pi/2

Hey guys, really struggling understanding how to go about this question :/ The full question is: "Let SIN(α)=a, where α is an element of (0, pi/2). Find, in terms of α, two values of x in [0, 2pi] which satisfies the equation SIN(x)= -a" I can see that SIN(x)=-SIN(α), but where do I go from...
7. ### Limit Involves Sine as x goes to Infinite

Find the limit of the following functions as x goes to Infinity. (a) f(x) = sin[ (x^2 + 4) / (x^2 - 4) ] (b) f(x) = (4 sin x)/x
8. ### area of region outside the circle by r =1 and inside the cardroid r = 1- sin (theta)

Find the area of region outside the circle by r =1 and inside the cardroid r = 1- sin (theta) Here's my working. but the ans given is 2 + (pi/4) unit ... Why am i wrong ?
9. ### 2 equations 2 unknowns

Please help me understand step by step how to solve this problem. I have 2 formula's with 2 unknows: 0.4*cos(a) - 0.3*cos(b) = 0.49 0.4*sin(a) - 0.3*sin(b) = -0.04 I have tried allot of things but i can't solve the problem :-( The teacher has given me the answer, so i can check that i get it...
10. ### Ration of sin of angles

In a \Triangle ABC\;, If \tan A:\tan B;\ \tan C = 1: 2:3\;, Then \sin A: \sin B: \sin C, is
11. ### cos x + sin x = 2x

I have two questions I can't figure out. 1. Solve on the interval 0 <= theta < 2pi 3 cot^2 theta - 4 csc theta = 1 2. Says solve using a calculator on the same interval. Round to two decimals. Cos x + sin x = 2x
12. ### Simplifying sin functions

This is for a Principles of Applied Mathematic college course. I am having trouble expressing sin((Pi/2)+iln5) as a simple fraction. My professor has given us the solution: 13/5, but no hints on how to get there. Thank you
13. ### y' + y = sin t

i have divided my working into 5 major parts , the third and fourth part is about the partial fraction . the answer given is -cos t +sin t + (e^-t) , but my ans is 0.5sin t + 0.5(e^t) +(e^t) -sin t . Which part of my working goes wrong ?
14. ### Why does this sequence converge? n * sin ( 1/n )

Hello, The back of my textbook says that this sequence converges and that its limit is 1. Can you explain this to me? I don't understand how to arrive at that answer. {an} = n*sin(1/n) What theorem, law, etc. should I apply?
15. ### dy/dx - y = sin x ( form differential equation)

i found that the integrating factor is (e^-x ) , so i gt y (e^-x ) = integral of sin x (e^-x ) , how to integrate sin x (e^-x ) ?
16. ### hypotenuse, adjacent, opp for cos 90+theta or sin 90 + theta.

How do you choose hypotenuse, opposite and adjacent side for cos 90+theta or sin 90 + theta in a circle? Similarly for sin 180- theta or cos 180 - theta in a circle.
17. ### prove of sin ( arc sec x )

can anyone?? i have tried out thr provoing , unfortunealy , i gt 1/x As we know that the cos theta is adjacent / hypotenuse . so i have sec theta = 1/ (cos theta) so i have hypotenuse /adjacent
18. ### integrate( x^2) arc (sin x )^3

how to do this ?
19. ### (sin x)^2 and sin (x^2)

What is the difference between (sin x)^2 and sin (x^2)?
20. ### implicit diffrentation e^ cosx + e^ sin y = 0.25

i have done 2 ways , but my ans isn't correct. can someone point out my mistake ?