What is Trig: Definition and 1000 Discussions

This is part of derivation of electric dipole potential where: V(\vec r,t)=\frac 1 {4\pi \epsilon_0} \left [ \frac {q_0 cos [\omega(t- \frac {\eta_+} c )]}{\eta_+}- \frac {q_0 cos [\omega(t- \frac {\eta_- } c)]}{\eta_-} \right ] \vec {\eta_+} = \vec r - \vec r^+ (t_r) \;,\; \eta...

Homework Statement \int xarcsin2xdx 2. The attempt at a solution Can someone explain to me what is happening at step 2? I understand how the integration by parts was done, but where does the (1/8) or (2x) come from?

Homework Statement \int\sqrt{4+9x^{2}}dx Homework Equations Pythagorean Identities? The Attempt at a Solution I find it sort of cumbersome to use the special formatting here, so I hope it is okay that I just photocopied my work on paper. You can see how far I made it, but...

Here's an interesting problem: How can you find the area of any normal polygon with x sides (or corners) that is inscribed in a circle of radius 1? No trig functions, or things like e or π (Pi), or infinite series, are allowed. If possible, try to avoid summation notation as well, but that might...

angle AOP is theta.. let the revolving line start on the pos y-axis and revolve through the angle theta in clock wise direction. the angle AOG is then 90 - theta.. I don't understand how angle AOG is 90 - theta.. it lookes like 90 + theta to me...?

when integrating by trig substitution why do you use what you use?? for example int. (1+x^2)^0.5 dx why do you use x= tan u i mean obviously because it works, but if you didn't know it works how would you figure it out? i would think that you should use x=sinh u but I've been trying...

My book was proving that.. sin(-x) = -sin(x) tan(-x) = -tan(x) cos(-x) = cos(x) .. I posted an attachment of the books explanation.. I just don't understand how their explanation has anything to do with sin of a negative angle equaling sin of an angle times negative one, the same goes for...

I am reading Eli Maor's Trigonometric Delights which is a fascinating story of the history of Trigonometry. I have a rather elementary question. On the early history: "To be able to do his calculations Hipparchus needed a table of trigonometric ratios, but he had nowhere to turn: no such...

So I've tried to wrap my head around this concept, and I just read the last two sections in this chapter in order to really get a proper mindset here. Despite reading, there are no examples in the book that pertain to these questions, nor is there anything saying what kind of problem it is and...

Can anyone tell me what the trig book is trying to tell me? Don't know what they mean by this? It says Finding other polar coordinate of a given point. Plot the point P with polar coordinates (3, pi/6) and find other polar coordinates for (r , theta) of this same point for which : there are 3...

Homework Statement angle 1 is 60 angle 2 is 25 and the suspended mass is 120kg CALCULATE THE TENSIONS FORCES A, B, AND C [PLAIN]http://img52.imageshack.us/img52/1412/unledfm.jpg Homework Equations The Attempt at a Solution I understand you have to use some triangles and some trigonometry. But...

I'm having a really hard time solving these word problems. ANY info on how to get the pictures drawn, which sides or angles to solve for, and instructions on how to solve would be greatly appreciated! 1. A tv antenna on top of a house is 4.50 ft tall. From a point on level ground the angles of...

Homework Statement How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ? Homework Equations The Attempt at a Solution Some kind of co-function identity?

1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) I got this far: 1-(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x) 1-(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x)

Homework Statement Find the derivative of y=5sin(0.5x+2)+6 Homework Equations My initial assumptions would be to use the chain rule. The Attempt at a Solution y=5sin(0.5x+2)+6 The chain rule is to take the derivative of the outer function and multiply by the derivative of the...

I'm stuck :/ I have to prove the following: sec (2x) - 1 = sin^2 x ____________ 2 sec (2x) Unfortunately, I don't know any terms that are equal to sec (2x). Any help would be awesome!

This may seem really simple, but I just can't figure out how to do it. Say you have an equation 0.651 = cos² (theta) How would you solve for theta in degrees? I know that for cos (theta) you take the arccos, but what do you do when it is squared? Thank you!

I know what sine is but I don't know what it really means! How do you get an angle from sin 1/2? Where is the process in between? Plugging it in the calculator doesn't quench my thirst for knowledge and mastery of it. I don't want to just know it, I want to completely understand it...

I'm following a worked example and really don't get a certain step in it: the step is going between r=(-(s-2a)sin($) , scos($)) and (r^2)=(s^2)+(4(a^2)-4as)sin($) First of all how do you 'square' coordinates? I would have though it stays as coordinates? Even when i try different...

if cos(theta)/sin(theta)=10.11, what is theta considering theta is a constant, just spent 2 hours on a collisions question and am stuck on the last hurdle, thanks for looking

Homework Statement Everyline tanjent to the function y=sin x has a y-intercept. Among all these tanjent lines, somewere between 0<x<2pi, find the equation of the line with the highest y-intercept. Homework Equations derivative of sinx=cosx Second derivative is -sinx The Attempt at a...

Cos(x/2) = 1/2 Trig Identity: Cos(x/2)= +- (1+Cosx/2)^(1/2) ..How do you know wheather to use the plus or minus of (1+Cosx/2)^(1/2) ? Do you only use the positive one because of the positive 1/2? Anyways... ((1+Cosx)/2)^(1/2) = 1/2 (1+Cosx)/2 = 1/4 1+Cosx = 1/2 Cosx = -1/2...

I don't really know if "easier" is the right word for this question, but I'm undecided about whether I should take trignonometry-based physics in order to get ready for calculus-based physics. I heard from numerous students that calc.-based physics is probably one of the hardest classes that...

Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part? if b = 2 , A =40 , find a,c, and B I found all of them except for c , how do you get c There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c Why do you...

Homework Statement If sin x = 0.3, cos a = 0.6 and tan t = 0.7, find the values of: a) sin (3pi/2 + a) b) cos (3pi/2 - x) I can't use use the formulas sin (a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a - b) = cos(a)cos(b) - sin(a)sin(b) because I don't some of the values But...

Sin \theta = -5/13, (3\pi / 2) < \theta < 2 \pi So I got cos \theta = - (sqrt 194) / 13 Is this the right answer?

Homework Statement ArcTan(-1) = theta I figured that theta was both 7pi/4 and 3pi/4.. but the book has -pi/4 Because my two answers are both equivalent to -pi/4 would I be wrong? Homework Equations The Attempt at a Solution

is it meaningful to evaluate cos and sin at infinity? I ask in relation to Fourier integrals... ie does cos(infinity) have a value

Cos70°cos20°-sin70°sin20° I can't find any of these angles that are equivalent to the basic angles. Thanks

Homework Statement The original problem wants me to simplify tan^2(x)-sec^2(x). I have simplified it down to (sin^2(x)-1)/(cos^2(x)). The answer says its solution is -1. My problem is I cannot understand how to get -1 out of (sin^2(x)-1)/(cos^2(x)). Thank you in advance. Homework...

Hello, I just started trigonometric functions, and the online learning tool keeps saying "incorrect" to sine2pi=0 and "incorrect" to cos2pi=1 Is this an error? Thanks :)

Homework Statement Show that cos^{2}(\theta)+cos^{4}(\theta)+cos^{6}(\theta)+cos^{8}(\theta)\approx 4cos^{4.3128}(\theta) , \mid\theta\mid\leq\pi/2 and cos^{2}(\theta)+cos^{4}+...+cos^{30}(\theta)\approx 15cos^{11.38211}(\theta) , \mid\theta\mid\leq\pi/2 Homework Equations...

Homework Statement Prove: tan( 45 + x) =cot( 45 - x ) Note: the numbers that I am using are in deg. Working with left side: tan( 90 - 90 + 45 + x ) =tan(90 - 45 + x) =tan(90 -(45+x)) =cot(45 +x) Is my algebra correct? If so why am I getting pos x and not a neg x? and if this is...

Homework Statement Math is not math when it asks me to describe relationships between functions. I hate wordplay. Please see the attached PDF. On this page it says "What relationship between the cosine and secant do the graph and these values suggest?" Homework Equations Well...

Homework Statement Using trig substitution integrate x2/(x4+6x2+9) Homework Equations The Attempt at a Solution I'm almost completely positive I need to use partial fraction decomposition... doing this I end up having the integral of 1/(x2+3)-3/(x2+3)2 There aren't any square...

Homework Statement Integrate (9x2-16)1/2/x4 Homework Equations The Attempt at a Solution I set 3x=4secy, 3dx=4secytany and (9x2-16)1/2=2tany. I then plugged that all into my integral and ended up with2tany*4secytany/(4/3secy)4 dy... (81/32) tan2y/sec3y dy... I solved for...

Homework Statement I am attempting to show that -x \leq sin(x) \leq x for x>0 and thus \int^1_0 nxsin(\frac{1}{nx})dx converges to 1. Homework Equations I know that I need to use the fact that I have shown that the limit as T tends to infinity of \int^T_1 \frac{cos(x)}{\sqrt{x}}dx...

Homework Statement sin(4s)/4 = cos^3(s)*Sin(s) - sin^3(s)*cos(s) In the book they did... 2*sin(2s)*cos(2s)/4 = 2*2*sin(s)*cos(s)/4 *(cos^2(s) - sin^2(s)) (I understand everything up until they multiplyed the 2*2*sin(s)*cos(s)/4 expression by cos^2(s) - sin^2(s)... where did cos^2(s) -...

Homework Statement Tan(15deg)/(1-Tan^2(15deg) In my solution manual this is what they did... 2/2 * Tan(15deg)/(1-Tan^2(15deg) = 1/2Tan(30deg) Ok first off... I noticed they multiplyed by a fraction of one (2/2) which resulted in 2*tan(15) in the numerator... ( I did...

Homework Statement ∫ dx/(x² -a² ) Homework Equations When (x² -a² ) appears in an integrand, you can use the trig sub: x=asecθ right? The Attempt at a Solution I know I could solve this using partial fractions but why doesn't trip sub work here? Or does it? I have attached my...

Homework Statement I need to solve this: cosx - cos2x + cos3x = 0 Homework Equations The Attempt at a Solution The solution shows something like: (cosx + cos3x) - cos2x Then using the sum to product on the first group and double angle on the cos2x. I would know to...

Tan theta=sin theta/cos theta What does that identity mean? What does it say about the triangle? And what on Earth is an identity? I understand everything taught in the course so far, trig ratios, reciprocal trig ratios, special angles etc etc...but i have no idea what identities mean, some...

Homework Statement Basically I need to solve for x that satisfies 2cosx - 2cos2x = 0 Homework Equations The Attempt at a Solution I changed it to 4sin(x/2)sin(3x/2) = 0 Then I know that sin(0) and sin(pi) = 0 So solve for x(1/2) = pi and x(3/2) = pi. I get 4pi/3 and the...

For some of the questions questions the initial arm is in the positive x and y quadrent and the terminal arm moves counter clockwise (+)this is considered positive , for some of them it is in the negative x and positive y quadrent, how does one determine where the initial arm is to be placed...

Homework Statement THIS PROBLEM HAS BEEN SOLVED Quoted verbatim: A ship has maneuvered to within 2500m of an 1800m high mountainous island, as shown below. If the shoreline on the other side of the island is horizontally 300m from the base, what are the distances from the shore at which...

Homework Statement A satellite dish that is 5m high sits atop a building, from a point at the base of building, the angles of elevation of the bottom and the top of the satellite dish are 39.1 degrees and 44.7 degrees. Determine the height of the building to one decimal place. Homework...

Homework Statement Suppose that the function f is defined on an interval by the formula f(x) = \sqrt{tan^{2}x - 1}. If f is continuous, which of the following intervals could be its domain? (A) (\frac{3\pi}{4},\pi) (B) ( \frac{\pi}{4},\frac{\pi}{2} ) (C) ( \frac{\pi}{4},\frac{3\pi}{4}...

Homework Statement I have to trig problems which I'm not entirely sure how to approach: 1) For which angles x is (sinx)^4-(cosx)^4 > (sinx)^2-(cosx)^2? 2) For what value x is the expression (sinx-cosx)^2+(sinx+cosx)^2 as large as possible? The Attempt at a Solution For...

Homework Statement Y = - sin (2X) Homework Equations The Attempt at a Solution So.. I know how to graph - sin, that's going to be one 1 but reversed. Now my problem is the (2x). How do I graph 2x in the trig graph? How would I go about making a horizontal compression? Thank you

My apologies. I'm not proficient with latex, and it is bogging my computer down for some reason today. Homework Statement intdx/\sqrt{(4-x^2)} [0, 2/sqrt{2} Homework Equations Trig Identity: a^2-a^2sin^2\theta The Attempt at a Solution In the interest of my own sanity I am going to...