What is Trig: Definition and 1000 Discussions

This is for Calculus II. I've found most of the integrations on inverse trig functions to be pretty simple, but for some reason this one is throwing me off. Homework Statement \int\frac{x+5}{\sqrt{9-(x-3)^2}}dx The Attempt at a Solution I started by breaking the integral up...

Hopefully this will make sense... We have the trig. identities shown below: sin(u)cos(v) = 0.5[sin(u+v) + sin(u-v)] cos(u)sin(v) = 0.5[sin(u+v) - sin(u-v)] How are these different? I realize u and v switched between the sine and cosine functions, but what is the difference between u and...

Homework Statement Cot^-1(-sqrt(3)) and CSC(arccos(3/5) Homework Equations The Attempt at a Solution I know this looks like a trig problem, but I'm in calc, just wasn't sure where to put this. I have the solution to both problems, my biggest issue here is that I do not know of...

Evaluate integral by using $x=3\sin{\theta}$ $\int{x^3\sqrt{9-x^2}}\ dx$ substituting $\int{27\sin^3{\theta}}\sqrt{9-9\sin^2{\theta}}\Rightarrow 81\int\sin^3\theta\cos\theta\ dx$ since the power of sine is odd then $81\int\sin^2{\theta}\cos{\theta}\sin{\theta}\ dx$...

1. what would be the limit?? without using the L'Hopital's rule lim_(x-0) (sin(3 x^2))/(8 x) the limit of sin(3x^2) divided by 8x as x approaches zero 2. Limits of trignometric functions 3. The Attempt at a Solution I tried factoring out the 1/8, but...

this is supposed to be solved with U substitution $\displaystyle \int \sin^6(x)\cos^3(x) $ since \cos^3(x) has an odd power then $\displaystyle \int \sin^6(x)\left(1-\sin^2(x)\right)\cos(x) dx $ then substitute u=\sin(x) and du=cos(x)dx $ \int u^6 \left(1-u^2\right) du $ so if ok so far

I'm taking my first semester of calculus based physics next week. How much trig should I know? I know the basics and inverse trig functions and stuff but should i know about trignometric equations, double angle and half angle formulas, product-to-sum and sum-to-product formulas? I passed both...

Problem statement Given sin theta (sqrt 3)/2 Determine the domain for the following solution https://www.physicsforums.com/attachments/655052) determine each general solution using the angle measure specified. Revelant equations Attempt at solution1What is the reasoning behind that? For...

## \frac {1}{4} \int sin^2 (2x)dx = I = \frac {1}{4} [- \frac {1}{2} sin(2x)cos(2x) + \int cos^2 (2x)dx]## when ##u = sin(2x), dv = sin(2x)dx, v= - \frac {cos(2x)}{2}## and ##du = 2cos(2x)dx## Now simplifying ##\int cos^2 (2x)dx## you get ## x - \int sin^2 (2x)dx = x - I## Then, ## I =...

Hi there, This is my very first post, so I'd like to say thanks for reading and hi basically. :biggrin: I'm relatively confident my attempt at the proof is correct, but since the method is quite different from other examples I have seen, it kind of makes me nervous. I was hoping someone...

For question 11 , how do you do part c? I know that (cos theta corresponds to x value and sin theta corresponds to y value. Using that I found the angle to be 318 degrees for part a. For part c, how would you start that? The answer is the coordinates flipped , x and y values with a positive...

Hello, Homework Statement find the general solution to cos3θ = sin2θ Homework Equations The Attempt at a Solution I know that sinθ = cos(π/2 - θ) but I am unsure of how to apply this when I have sin2θ. Do I say that sin2θ = cos2(π/2 - θ)? I think not because when I do...

In order for an equation to be a function, it has to pass the vertical line test. A circle is not a function because it does not pass the vertical line test. A curve containing a loop does not pass the vertical line test and to me that means it is not a function. However, if I am given...

Homework Statement A mine shaft is 320 m in length and descends 74 meters. Find the angle of inclination. Homework Equations sin=opp/adj The Attempt at a Solution inverse sine=42/320 inverse sine*.231=13.37 degrees. The answer seems conceivable.

Not homework just my own revision. If sin a = –cos b = 3/5 and a and b are both in the second quadrant, what is cos (a – b)? Now keep getting the answer 0, but the answer is apparently 24/25, now they use the trig subtraction formula, I just did cos ((arcsin(3/5) - arccos(-3/5)) I got 0 as...

Homework Statement Solve sin2θ - 1 = cos2θ in range 0 ≤ θ ≤ 360° Homework Equations The Attempt at a Solution I always struggle with the end of these questions, deciding which answers are correct. Here's what I have done; let 2θ = x cosx + 1 = sinx cos2x + sin2x = 1...

Hi I was wondering how calculators calculate trigonometric functions. Do they use taylor polynomials(if so what order) or what? any help appreciated.

Homework Statement A patrol car is 50 ft from a long warehouse. The revolving light on top of the car turns at a rate of 30 rotations per minute. How fast is the beam of light moving along the warehouse wall when the beam makes a 45° angle with the line perpendicular from the light to the...

Homework Statement If [sinx]+[√2 cosx]=-3, x belongs to [0,2∏] (where [.] denotes the greatest integer function) then x belongs to 1)[5∏/4,2∏] 2)(5∏/4,2∏) 3)(∏,5∏/4) 4)[∏,5∏/4] The Attempt at a Solution If I put x=5∏/4, LHS=-2 which does not satisfy. 2∏ and ∏ also does not...

Homework Statement To show that sin A + sin B = +2|sin ((A+B)/2)*cos((A-B)/2)| is easy. However, it is not clear how to remove the absolute value signs to give the valid identity sinA + sin B = 2(sin ((A+B)/2)*cos((A-B)/2)) without having to go through many cases. Homework Equations...

Couldn't figure out why. Where 0.27 deg =3pi/2000. Now the only way I could figure this out is 270 deg = 3pi/2. multiply by 1000 to get the 270 and the 2000, but gives 3000pi/2000? Anyone tell me where this came? Thanks

Inverse trig problem -- please help! Homework Statement tanx+tan2x+root3tanxtan2x=root3 find x... Homework Equations The Attempt at a Solution i have tried a lot and always ended with a complicated cubic equation... please help me by giving me a another approach to the solution

Homework Statement sec(5x)-5=0 Homework Equations The Attempt at a SolutionI turned it into 1/cos(5x)=5 x=θ/5 then i switched it to cos(5x)=/1/5 Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution since the positive cos is in the 1st...

Homework Statement Write sin(7t)-sin(6t) as a product of two trig. functions. Homework Equations e^(ix)=cos(x)+isin(x) sin(2x)=2cos(x)sin(x) cos(2x)=cos^2(x)-sin^2(x) The Attempt at a Solution I do not really know how to approach this. I have tried using the sin(2x) identity...

Homework Statement Solve cos(3θ) = 0.85 in the range 0 ≤ θ ≤ 360° Homework Equations The Attempt at a Solution cos(3θ) = 0.85 3θ = 31.79° θ = 10.6° (3 s.f) I have drawn my transformed cos curve, where the full wave completes after 120°, so there are 3 full cycles in my...

Homework Statement http://i.minus.com/iCJwlfzPc5fRu.png Homework Equations This feels like a movie requiring the suspension of disbelief. The Attempt at a Solution cot(x) = cos(x)/sin(x). cot(0) = 1/0 Right? How in the world then is 0cot(0) - 1 = 0? That should be infinity minus 1.

An astronaut arrives on the planet Oceania and climbs to the top of a cliff overlooking the sea. The astronaut’s eye is 100 m above the sea level and he observes that the horizon in all directions appears to be at angle of 5 mrad below the local horizontal. What is the radius of the planet...

Homework Statement Evaluate the following exactly. cos 300° sin(-120°) Homework Equations Unit circle The Attempt at a Solution I seem to have a problem with the remembering if it is going to be the position on the unit circle such as in these cases I thought it was cos 300°=...

Homework Statement Simplify cot(θ)sin(-θ) so that it is a single trig function of positive θ Homework Equations The Attempt at a Solution I changed cot(θ) to cos(θ)/sin(θ) X Sin(-θ)/1 I stated that sin(-θ) and sin(θ) were the same and then cancled out the sin(θ) and sin (-θ) to...

Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...

The question is "Find the real solutions θ for both of the following, a. sinθ=1/2, b. sin(7θ)=sin(5θ)" On part a, I know that theta must be 30° or π/6 but I know that I need to mathematically show it and not sure how. And part b just has me head spinning, don't know where to start on that one.

∫x3 ---------------------- (4x2 + 9) 3/2 According to my book this is a trig substitution integral. The normal procedure is to substitute atanθ for x when one has a square root w an argument of the form x^2 + a^2. Because the argument of the square root is 4x2 + 9, as opposed to simply x2...

again, i need some help here guys.$\displaystyle\int\frac{3x-1}{2x^2+2x+3}dx$ =$\displaystyle\int\frac{3x-1}{2\left[\left(x+\frac{1}{2}\right)^2+\frac{5}{4}\right]}dx$ $\displaystyle a=\frac{\sqrt{5}}{2}$; $\displaystyle u=x+\frac{1}{2}$; $\displaystyle du=dx$; $\displaystyle x=u-\frac{1}{2}$...

Hi guys, Can you help me I am stuck: By finding the real and imaginary parts of z prove that, $$|\sinh(y)|\le|\sin(z)|\le|\cosh(y)|$$ i have tried the following: Let $$z=x+iy$$, then $$\sin(z)=sin(x+iy)=\sin(x)\cosh(y)+i\sinh(y)\cos(x)$$ $$|\sin(z)|=\sqrt{(\sin(x)\cosh(y))^2+(\sinh(y)...

another trig problem that i tried to solve. just want know an alternative way of solving this without using product formula. $\displaystyle\int \sin(3x)\cos(5x)dx$ anyways this is how i solved it $\displaystyle\int\frac{1}{2}\sin(3x-5x)+\frac{1}{2}\sin(3x+5x)dx$...

Homework Statement Homework Equations The Attempt at a Solution This isn't really a traditional question, but can someone explain to me how substituting u = tan^-1(x/y) got to that final value? I'm trying to understand this for an exam coming up.

Consider a trig function such as: y = A cos (bx - c) For the phase shift, we would use (-c/b); which aligns with the original function equation and makes sense to me. But in the case of a trig function such as: y = A cos (-bx + c) For the phase shift, we would use (+c/-b); which would...

hey guys can you help solve this problem. $\displaystyle\int\frac{dx}{\sqrt{2x-x^2}}$ i know that i have to change the integrand into this form $\displaystyle\frac{du}{\sqrt{a^2-u^2}}$ can you please show me how. thanks!

when working with trig functions. is there a trick to knowing if there are 2 solutions while filling out a triangle without memorizing your sines and cosines. or do I need to be subtracting all numbers I get by 180 then sin/cos them to see if they have the same number? doing law of sines right...

Hey guys, I just wanted to come here and see if anyone could help me out. I am getting stuck using the trig formulas for summing sines and cosines. I won't beat around the bush too much, so let's get right into it. Homework Statement Use a trig formula to write the two terms as a single...

Homework Statement Integral of dt/ (√(t^2 -6t + 13) Homework Equations I sub v = t-3, and v = 2tan(θ) The Attempt at a Solution first I completed the square of t^2 -6t + 13, I got (t-3)^2 +4 Also I say v = t-3 ∫ dv/ (√(v^2 +4) I then sub in trig ∫(2sec^2(θ)dθ / 2√(tan^2(θ) +1) = ∫...

Homework Statement I have two questions sin2x = 1/25 and this obviously becomes sinx= +-(1/5) I also have cos2-1.5cosx-0.54 and cosx = (-3/10) and (9/5) Now this is asking for me to solve for the x value in radians in the domain [0,2pi] and I have no idea how to solve these for exact values...

SOLVED! :) Homework Statement The question is as follows; Prove that (tan(A+B)-tanA)/1+tan(A+B)tanA = tanB Homework Equations I'm certain the addition fomulae need to be applied, although I'm not entirely sure how. I genuinely have tried many times! The Attempt at a Solution...

I've got this problem right now, which asks me to prove that $$Ccos(\omega_{o}t-\phi)=Asin(\omega_{o}t)+Bcos(\omega_{o}t)$$ This proved to be a bit more difficult than I expected, so I looked up a complete list of trig identities. $$cos(a\pm{b})=cos(a)cos(b)\mp{sin(a)sin(b)}$$ seems like the...

Homework Statement Did I make a mistake here somewhere? The solution in the back of the book is completely different. Seems like they used trig sub one step later or something. I can't find any error in my logic. Test coming up soon and I'm confused and panicking -_-! Actually I just found a...

I recently have been teaching myself vector calculus online, i am by no means a master but i get the general concepts. I know you can use it to solve the motion of a particle in a fluid and was curious as to whether it can be used to solve simple physics problems, involving current and wind...

Its the attached picture. I'm not seeing why when using the dot product, they start using sin.

Homework Statement We have cosx = -5/6 in the third quadrant, and I solved for sin(x/2). I did sin^2(x/2) = 1-cos(x)/2 --> I get to sin^2(x/2)= 11/12, and here's my question. When rooting I should choose the negative value because sine is negative in the third quadrant right? But in...

Homework Statement Prove that the set of all trigonometric polynomials with integer coefficients is countable. Homework Equations t(x)= a+\sum a_ncos(nx)+ \sum b_n sin(nx) the sum is over n and is from 1 to some natural number. The Attempt at a Solution So basically we have to look at all...

How does this work? I'm very confused about the phi is solved using inverse sin. knowing: A=(c^{2}_{1}+c^{2}_{2})^{1/2} and c_{2}= Acos(\phi) solve for \phi which yields: \phi=sin^{-1}\frac{c_{2}}{(c^{2}_{1}+c^{2}_{2})^{1/2}}=tan^{-1}\frac{c_{2}}{c_{1}} I'm not sure how we use the inverse...