What is Trig: Definition and 1000 Discussions

Homework Statement Proof that (1/6)sin(3x)-(1/18)sin(9x) = (2/9)sin^3(3x) Homework Equations The Attempt at a Solution I am just curious exactly how the power on the sine function is cubic on one side. It obviously has to do with something that increases the power on the...

Question Find all the values of ∏ in the interval 0 < θ < 2∏ for which 2cos2 θ – sin θ = 1, giving each answer in terms of ∏ I think the question is asking me to find the values of θ in terms of ∏ for all values between 0 < θ < 2∏ This is what I have done so far I have worked...

Would someone kindly take a look at my geogebra snapshot attached, and tell me a more formal way of representing the formula for the period of a trig function of form: f(x)=Acos(bx)$$ where A is amplitude and b is period Thanks, D'abs http://www.mathhelpboards.com/images/mhb/misc/paperclip.png...

For some polynomial functions it is useful to logarithmize both sides of the eq. First. How can this be applied for inverse trig functions? Is it even possible?

Find the derivative of y = arctan(x^(1/2)). Using the fact that the derivative of arctanx = 1/(1+x^2) I got: dy/dx = 1/(1+abs(x)) * (1/2)x^(-1/2) But my textbook gives it without the absolute value sign. I don't understand why because surely x^(1/2) squared is the absolute value of x...

Homework Statement f(x) = cos^2(x) - 2sin(x) 0≤x≤2∏ Homework Equations The Attempt at a Solution f'(x)=-2[(cosX)(sinX) + cosX] f''(x) = -2[ (cos^2(x)-sin^2(x)-sinX] I know there's an identity there for cos2x but it doesn't seem to help me. I also tried to go the other way...

Q If cos(alpha)=-sqrt3/5 and alpha is in the third quadrant, find exact values for sin(alpha) and tan(alpha). A. Well what I did was use the pythagorean theorem so (-sqrt3)^2+(opposite)^2=5^2. then in the end I got sqrt22 for opposite so then sin(alpha)=sqrt22/5 and tan alpha =sqrt22/-sqrt3...

Homework Statement Show that: $$\tan x\sec^4x\equiv\tan x\sec^2x + \tan^3x\sec^2x$$ Homework Equations Trig identities / formulae The Attempt at a Solution I've got 2 different starts for it but I'm stuck after a few steps with both of them: Attempt 1: $$\tan x \sec^4...

There are currently some changes happening in Texas and math courses are being revamped from Trig on up to cal III at some community colleges. I am in college algebra right now and have a pretty good average thus far this semester. I was wanting to take trig in Summer one and take precal in the...

Homework Statement I came across a question like this on a test today, and it says it would be helpful to simplify before differentiation. However, I could not find ways to simplify (1- cos(x))/(1+cos(x)). Homework Equations ln((1- cos (x))/(1+cos(x)))^7) The Attempt at a Solution...

Homework Statement Prove the identity: $$\csc(2\theta)-\cot(2\theta)\equiv\tan(\theta)$$ Homework Equations The Attempt at a Solution Starting with the LHS: $$\csc(2\theta)-\cot(2\theta)$$ $$\frac{1}{\sin(2\theta)}-\frac{\cos(2\theta)}{\sin(2\theta)}$$...

Homework Statement i'm confused as to why a molecule with 3 bonding pairs and 2 lone pairs takes on a t-shape rather than a trigonal planar shape. My notes say that this is because in a t-shape, there are less 90 degree angles between the lone pairs and the bonding pairs than in a...

[SOLVED]Trig problem: max square cut from circle Since this one is homework related, ill ask this as a procession so that I can make sure that I am grasping the logic. the question is that with a round log with a diameter of 16cm, what is the strongest log that can be cut where the strength =...

Hey guys! I'm stuck on a Laplace transform. Following is the problematic function: [cos(t)]^3 Seems simple, but I'm having issues doing the Laplace transform on odd trigonometric functions. When I use the half-angle formula, I get this, which I can't seem to solve: 1/2cos(t) +...

Hi, here I come again now with a problem, this time is more because the boo didn't really explain much deeper than the minimum. This time it's not homework related ... Yet. Lol. I just wanted to know how I would separate an equation like y=sin^2x cos3x To find the derivativ; I guess how...

Homework Statement Evaluate the integral. Homework Equations \displaystyle\int \frac{1}{x^5 + 5} dx The Attempt at a Solution could i turn this into an x^2 + a^2 --> arctan for example: \frac{1}{x^(5/2)^2 + \sqrt{5}^2} dx note that is: x^{5/2} squared.

Homework Statement Find the volume obtained by rotating the following curves bounded by: y=sinx y=0 pi/2≤ x ≤ pi Homework Equations I know I have to use the cylindrial disk method so ∫2pi(x)f(x)dx. The Attempt at a Solution I did the following ∫(pi/2 to pi) 2pi (x) sinxdx...

Homework Statement consider the region bounded by the graphs of y=arcsinx, y=0, x = 1/2. a) find the area of the region. b) find the centroid of the region.Homework Equations \displaystyle\int_0^{1/2} {arcsinx dx} u=arcsinx; du = \frac{1}{1-x^2}dxdv=dx ; v=x xarcsinx]^{1/2}_{0} -...

Could anyone help me out with this: Which of the following statements are true and which are false? Justify your answers. iii) There exists a polynomial P such that |P(x) - \cos(x)| \leq 10^{-6} I've tried to thinking about it, and it seems as though it is false, because |cos(x)|...

Homework Statement Prove the following: tan2A=2tanA/1-tan^2A Homework Equations The Attempt at a Solution Took the right hand side: =2(sinA/cosA) / 1-(sin^2A/cos^2A) =2sinA/cosA /cos^2A-sin^2A/cos^2A =2sinA/cos2A /cosA/1 Dont know what to do next?

Homework Statement ∫(x+1)/((x^2+1)^2) Homework Equations The Attempt at a Solution I have been able to separate this into 2 ∫x/(x^2+1)^2 dx which i found to be equal to (1/2)arctanx and ∫1/(x^2+1)^2 dx which i am unable to find What i did was sub in x=tanθ and dx=sec^2(θ)dθ, and with...

Homework Statement lim 2x/(sin3x) x-> 0Homework Equations lim sinx/x = 1 x->0 The Attempt at a Solution is it correct to say the following: lim 2/3 (sinx/x) x-> 0 lim 2/3 (1) x-> 0 Answer: lim 2x/sin3x = 2/3 x-> 0 Because it's on the book: cos 2x(2)/3...

Homework Statement Use a trigonometric substitution to evaluate the integral. Homework Equations \int e^x\,dx /\sqrt{1-e^2x} The Attempt at a Solution e^x = sin∅ x=lnsin∅ dx=cos∅/sin∅ \frac{sin∅*cos∅}{sin∅*\sqrt{1-(sin∅)^2}} \int sin∅cos∅ / sin∅(cos∅)\,d∅...

Homework Statement See attached image. Homework Equations Sine law Cosine law The Attempt at a Solution I'm really not sure what to do on this one. I know that the angle ABC and ACB will be the same, but after that I'm stumped. It's been a long time since I've taken a math course...

$$\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)}$$ progress: I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$

Homework Statement use l'hopital's to evaluate the limit. Homework Equations limit (∅->0) ∅-3sin∅cos ∅ -------------------- tan∅- ∅ The Attempt at a Solution i take the derivatives of the top and bottom, and use...

Hi all.. another Trig question here... Let's say I'm given a graph of a sinusoidal function and asked to find its equation, but I'm not told whether this is a sine or cosine function and I'm left to determine that myself. I understand that evaluating where the graph intersects the y-axis is...

Homework Statement If x = asecθ, y =btanθ show that dy/dx = (b/a) cosecθ and d2y/dx2 = (-b/a2)cot^3θ The attempt at a solution I got the 1st part dy/dx = (dy/dθ) * (dθ/dx) = bsec^2θ x 1/(secθtanθ)= (b/a) cosecθ Now I tried differentiating a 2nd time and I don't get...

Homework Statement x3 - sin 2x Find f'(∏/6)The Attempt at a Solution f'(x) = 3x2 - 2 cos 2x f(∏/6) = 2700 - 2 [ (√3/2) ] ---> from 2 [ cos(∏/6)] answer: 2700 - √3 My book has the answer as (∏2 - 12)/12

Homework Statement 1. f(x) = 5 sin (8∏x) 2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)] 3. h(x) = cos [sec (5∏x)] 4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection. f(x) = 2sinx + sin2x ; [0,2∏] The Attempt at a...

Homework Statement y = √sinx The Attempt at a Solution y' = [(sinx)1/2]' y' = 1/2 (sinx)-1/2 (sinx)' y' = 1/2 cosx (sinx)-1/2 However book says the answer should be: 1/2 cotx (√sinx)

Am I doing this correctly. x \tan=\frac{183}{\tan 30}=317ft Also if it were the other way around and I needed to find the height but I already had the length would it just be h \tan=\frac{x}{\tan 60}=hft

Homework Statement evaluate the integral. Homework Equations integral (x^3 / (x^2 - 16) The Attempt at a Solution x=4sec∅ dx=4sec∅tan∅d∅ 1. i substituted those values in, and then split sec^4∅ into sec^2∅ and (1+tan^2∅). 2. integral 16 (1/u) du + integral 16 (u) du. 3. end...

Homework Statement Find tan A, tan B I have a right angle triangle. Length a = t, length b = k, hypotenuse = p. The Attempt at a Solution Usually I would just use the normal rule of \tan a =\frac{opp}{adj} but how can I get an answer here? I can't just say \tan a =\frac{t}{k}...

Am I doing good on this problem?

Homework Statement integral of dx/((9-(x^2))^(3/2)) A = 0, B = 3/2 Homework Equations Trigonometry Substitutions 3. The Attempt at a Solution : I am stuck with this question. So far, I got (1/9)integral of (1/cos^2(θ)) dθ

What identity I need to use for simplifying this trig expression into one expression?$cos(3x)+4hcos(x)$ where h is a constant. Thank you for your help. Can you explain, too?

cosθ + sinθ = √2 cos(θ-∏/4) what are the steps in between?

Hi, So I'm stuck on a part of trig which I can't seem to wrap my head around. I'm self teaching so no teacher to ask unfortunately. The question(s) come in the form: "Find the the max and min value of each of the following functions. In each case, give the least positive values of x at which...

Homework Statement I have to use this in my calculation \theta=\tan^{-1}\left(\frac{19 \pm 1}{47 \pm 1}\right) where both are in mm. How would I get this into \theta\pm \text{error}? Homework Equations shown above The Attempt at a Solution looked through my lab manual, it wasn't...

I hope this isn't too simple for the maths forum. I'm trying to find the length of the locus described by the bottom of a garage door as it is raised. It's all fairly straightforward until I have to integrate a function of the form √ (sin2θ + k cos2θ) k does not depend on θ. I tried...

Homework Statement Evaluate the definite integral ∫85/√(32-20x-25x^2) Homework Equations The Attempt at a Solution I started off this question using the completing the square method, and was able to simplify my integral to the point 17∫1/√(36-u^2) du where u is 5x+2 and du...

Homework Statement ∫sin(t)cos(2t)dt Homework Equations cos(2t)=1-2sin^2(t) The Attempt at a Solution ∫sint(t)(1-2sin^2(t))dt but where do i go from here? i can't use substitution. or parts?

Homework Statement \int \frac{dx}{\sqrt{x^{2}+16}}Homework Equations The Attempt at a Solution x=4tan\theta dx=4sec^{2}\theta d\theta Therefore: \int \frac{4sec^{2}\theta d\theta}{\sqrt{16tan^{2}\theta +16}} = \int \frac{sec^{2}\theta d\theta}{\sqrt{tan^{2}\theta+1}} \int \frac{sec^{2}\theta...

Homework Statement attachment Homework Equations The Attempt at a Solution ok can someone explain to me how this is done. I have no idea how in hell it got broken into those two.

Homework Statement \int_{-p}^{p} \frac{2p}{(1+v^2)\sqrt{p^2 + v^2 +1 }} dv Homework Equations 1 + \tan{\theta}^2 = \sec{\theta}^2 The Attempt at a Solution I thought the best way to go about this was to rename some constants. Let \alpha^2 = 1 + p^2 so that we are left with...

Homework Statement Posted #39 and $41. (look at the attachment). ds = distance from the radiation source to the skin dt = distance from the outer layer of the skin to the targeted issue 2fs = field size of the skin 2fd = targeted field size Homework Equations None The...

Ok I have this equation which is x\sqrt{1-y^2}dx = dy that I have to solve. I solved it and got \frac{x^2}{2} = arcsiny + c I think that's right. Now the next part of the equation requires me to find the solution of this equation that passes through the point (0,1). That means I plug...

Homework Statement Consider the region of the x-y plane between the line y=7, the curve y=3sin(x)+4 , and for -pi/2<x<3pi/2 Find the volume of the solid generated by revolving this region about the line y=7. I know that for this problem, I will be using the disk method (as the title...

Homework Statement Simplify (2cos2x-cos4x)/(2cos2x+cos4x) The Attempt at a Solution I let θ = 2x (2cosθ-cos2θ)/2cosθ+cos2θ) Since cos2θ= 1-2cos^2 (2cosθ-(1-2cos^2)/2cosθ+1-2cos^2 But I get lost when applying it and can't get beyond this, Do i have to use the quadratic...