What is Trig: Definition and 1000 Discussions

I have researched this area a little bit and now I am a little worried because three different websites have gave me three different answers. Some functions matched, but others didn't. My general consensus is inverse Sin= 1 and 4 quad inverse Cos= 1 and 2 quad inverse tan= 1 and 4 quad...

Homework Statement Lim (cosθ-√3/2)/(θ-pi/6) θ→pi/6 Homework Equations The Attempt at a Solution My attempt at this has been to try to multiply both the numerator and denominator by either the numerator's or denominator's conjugate. both result in 0 at the denominator. I also...

srirahulan's question on Math Help Forum, Hi srirahulan, Consider the left hand side of the above equation, \begin{eqnarray} \frac{\sec 8A-1}{\sec 4A-1}&=&\frac{\cos 4A}{\cos 8A}\left(\frac{1-\cos 8A}{1-\cos 4A}\right)\\ &=&\frac{\cos 4A}{\cos 8A}\left(\frac{2\sin^{2} 4A}{2 \sin^{2}...

Homework Statement Find the exact value of: sin (-5∏/12) 2. The attempt at a solution sin (-45° + -30°) = sin -45° cos -30° + cos -45° sin -30° = (sqrt (2) / 2 )(sqrt (3) / 2 ) + (sqrt (2) / 2)(1 / 2) = (sqrt (6) + sqrt (2)) / 4 However, the book has (-sqrt (6) -...

Homework Statement The problem along with its solution is attached as Problem 1-5.jpg. Homework Equations Trigonometry. The Attempt at a Solution Should the 60° angle in Fig. 3 be 30°? Is Fig. 3 supposed to be the exact same thing as Fig. 2 except that the force is moved to be entirely...

Homework Statement Amateur astronomers often approximate angles with an arm out- stretched. With the hand in this position, one finger's width is approximately 2 degrees, the width of your hand at the knuckles is approximately 10 degrees, and your hand fully spanned is approximately 20...

Homework Statement I just need to find the anti-derivative of this equation: \int x(sin^2(3x)cos(3x))dx Homework Equations sin^2(x)+cos^2(x)=1 The Attempt at a Solution I'm not really sure where to start here. I tried to do a substitution first but couldn't make it work. So then...

From my Math Textbook Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of 20 degrees. Paris is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of 18 degrees. Romeo and...

Homework Statement solve 5sinx +12cosx =6.5 between 0 and 180 degrees Homework Equations The Attempt at a Solution i tried squaring both sides. (5sinx +12cosx)^2= (6.5)^2 25sinx +60sinxcosx +60sinxcosx + 144cosx^2 =42.25

I wanted to try an alternative method to the proverbial technique used in trig substitution. Is this method a dead-end or is there hope for it? \int \frac{\sqrt{x^2-3}}{x} dx Using trig substitution c^2=a^2+b^2 a = \sqrt{c^2-b^2} ∴ c = x, b = \sqrt{3} Assigning these values to a triangle...

Homework Statement A vacation resort in a mountain town has installed a zip line( a sturdy wire, down which costumers in harnesses can quickly descend from high altitudes) to attract patrons. One zip line is 1,750 feet long and allows its rider to descend from a ski slope down to the ground, a...

I'm a bit rusty.. I have a cosine y = cos(2*pi*f*t) If I want to advance the cosine by say 90 degrees y = cos(2*pi*f*t + pi/2) but.. this waveform has f cycles per 2*pi*t..so won't I be advancing the phase by f*pi/2? someone pls straigthen me out - I'm working with Matlab indexes and...

Hello, I am trying to integrate 1/(x^2-1). Apparently this can be solved by using trig substitution involving tan ? Can someone please help me to understand how to go about it. Thanks kindly for any help.

I'm still trying to figure out how to do limits of trig functions and I would like to know if this is the correct approach. I know the answer is correct, but not sure if that is just a coincidence. Homework Statement lim (x -> 0) of (sin 2x) / (sin3x). Homework Equations The Attempt at a...

$z\cos z$ Let $z = x + yi$. Then $f(z) = (x + yi)\cos (x + yi)$. By the addition rule for cosine and the identities $\cos yi = \cosh y$ and $-i\sin yi = \sinh y\Leftrightarrow \sin yi = i\sinh y$, we have that $\cos (x + yi) = \cos x\cosh y + i\sin x\sinh y$. So $$ f(z) = z\cos z = x\cos x\cosh...

hey, If you have say, cos(x+β) where β is the phase and it fluctuates randomly (not just small fluctuations large ones) between 0 and 2∏ the average value of cos(x+β) would still be 0 right? thanks

Homework Statement Use fundamental identities to simplify the expression: (sinx)^2 - (cosx)^2 ____________________ (sinx)^2 - (sinx cosx)*note: it's a numerator and denominator. The underscore line is the fraction line. *note: The answer in the back of the book is "1 + cotx" but I would...

When I was checking my work, Wolframalpha took my trig work a step further with an identity that no one in my Calculus II class has ever seen, including my teacher. csc(2x) - cot(2x) = tan(x) I tried to prove the identity myself and I looked online, but no luck. Please, could someone...

I have been working on showing the equality between N=0 to ∞ Ʃ cos(2nθ)(-1)^n/(2n)! = cos(cos(θ))cosh(sin(θ)) I started by using the standard series for cosine and putting cos(2nθ) in for the x term. I did the same for cosh(sin(θ)). I manipulated the forms every way I could think but...

Homework Statement Simplify the expression Cos(6θ) Simplify means - the angle for all trigonometric functions in your answer is to be only θ. Simplify in terms of sines and cosines Simplify in terms of cosines only Simplify in terms of sines only Homework Equations Basic Trig Identities...

Homework Statement The roof of a ski cabin has a steep pitch to help snow slide off. What angle does the roof make with the horizontal? Homework Equations SOH CAH TOA The Attempt at a Solution I don't really know where to start considering I have no numbers to play around with so...

Homework Statement Find all possible solutions: 2cos22θ = 1 - cos2θ The Attempt at a Solution I know all my arithmetic is correct, but when it comes to giving the answer, I'm not sure how to write it. 2cos22θ + cos2θ - 1 = 0 (2cos2θ - 1)(cos2θ + 1) = 0 2cos2θ = 1 cos2θ = 1/2 2θ =...

Homework Statement Problem 4: http://www.nspsmo.org/_data/global/images/2010-11%20Sample%20Problems.pdf Homework Equations Second to last page in same document. The Attempt at a Solution I know how to solve everything but the minor chord lengths: CD, DE, EF The only thing I could think of...

Homework Statement Hello, I am trying to simplify the inputted function here http://www.wolframalpha.com/input/?i=sqrt%282%29+sqrt%281-cos%28%282pi%28x-y%29%29%2Fn%29%29 which is \sqrt{2}\sqrt{1-cos[2\pi(x-y)/n]} to the form of 2sin[(x-y)\pi/n] Homework Equations Not sure The Attempt at a...

Homework Statement A lens with radius of curvature R sits on a flat glass plate and is illuminated from above by light with wavelength λ (see picture below). Circular interference patterns, Newton's Rings, are seen when viewed from above. They are associated with variable thickness d of the...

Homework Statement An isosceles triangle has a rectangle inside of it with length 2 cm and width 6 cm. What angle ∅ will give the triangle the minimum area. Homework Equations A =1/2 (bh) The Attempt at a Solution

hey guys, I've been trying to solve this question, http://img515.imageshack.us/img515/2583/asfj.jpg so the general solution would be y(cos(theta)) = C Pn(cos(theta)) + D Qn(cos(theta)) right? and since n = 2 in this case y(cos(theta)) = C P_2 (cos(theta)) + D Q_2...

Hello! I've been tackling the question 'Express sin3x+sinx as a product and hence solve 1/2(sin3x+sinx)=sin2x ; x∈R' but I'm stumped - I'm not sure whether I've even approached it correctly. This is what I did: sin(3x+x)=sin3x.cosx+sinx.cos3x inserting this into the second equation...

Homework Statement If Sin(u)=\frac{\sqrt{2}}{2} and cos(v)=\frac{4}{5} and 0≤ u ≤\frac{∏}{2} and \frac{3∏}{2}≤ v ≤ 2∏ find cos (u+v) The Attempt at a Solution cos(u)=\frac{\sqrt{2}}{2} and cos(v)=\frac{4}{5} Do I just add them together? I feel like I'm missing something, but maybe the...

Homework Statement Hi, How do I solve for y in this triangle? (picture in attachment) Homework Equations So I use the special angel ratio and get sqrt(3)x = y + 20 and then from the smaller triangle I get tan(theta) = 20 / x What do I do next? Thanks. The...

Our teacher used the following on a problem solution: cos(x-a)cos(b-x) = \frac{1}{2}[cos(a+b-2x) + cos(a-b)] Where does this come from? I can't find it in anywhere (except for wolframalpha). Thanks.

Homework Statement I need to find at least two values of x in the interval [0,∏/2] for which f(x)= sin(x)+sin(2x)+sin(3x)=1 The Attempt at a Solution now this is what my understanding is and this is what I have done sin(x)+sin(2x)+sin(3x)=1 sin(x)+sin(2x)+sin(3x)-1 Now by...

Hi, I have a simple question i am working a tension query and need to do some trig calculations. I know the equation i need is below. θ = Sin^{}-1 0.6/3 When i type this in the calculator as shown above i get an answer of 12.29 although when i enter it in the calculator using brackets...

Homework Statement Suppose c and (1 + ic)^{5} are real, (c ≠ 0) Show that either c = ± tan 36 or c = ± tan 72The Attempt at a Solution So I considered the polar form \left( {{\rm e}^{i\theta}} \right) ^{5} and that \theta=\arctan \left( c \right) , so c = tan θ Using binomial expansion, I...

Homework Statement This question is part of Fourier Series in Circuit Analysis. There were fairly straightforward integrals which I calculated and confirmed using MAPLE to be correct, however the book gives somewhat different answers. I would presume that what I did was correct and the...

Homework Statement cosθ = sin2θ/2 Homework Equations None. The Attempt at a Solution I really don't know what to do. I tried using the half and double angle identities and this is what I got: cosθ = (1-cos2θ)/2 2cosθ = 1-cos2θ 2cosθ + cos2θ = 1 2cosθ + 2cos2θ -1 = 1 2(cosθ +...

Homework Statement \frac{cos^{2}t+tan^{2}t -1}{sin^{2}t} = tan^{2}t Homework Equations Here are all the trig identities we know up to this point (the one's that we have learned so far, obviously we derive many others from these when verifying identities). Pythagorean Identities...

prove 1-(cos(x)+sin(x))(cos(x)-sin(x))=2sin^2(x) foil out the center I get 1-cos^2(x)-cos(x)sin(x)+cos(x)sin(x)+sin^2(x) the -cos(x)sin(x)+cos(x)sin(x) cancels to 0 leaving 1-cos^2(x)-sin^2(x) then I'm lost... I know I can switch 1-cos^2(x) to sin^2(x) but that doesn't help...

Homework Statement \stackrel{lim}{x\rightarrow 0}\frac{cos^2x-1}{2xsinx} Homework Equations \stackrel{lim}{x\rightarrow 0}\frac{1-cosx}{x}=0 \stackrel{lim}{x\rightarrow 0}\frac{sinx}{x}=1 The Attempt at a Solution I found this problem online (and can't remember where). It...

Homework Statement How do I get y'' - yω2 = y'(sinωx + sinhωx) + y(cosωx*ω + coshωx*ω) equal to y'' - yω2 = sinωx + sinhωx I'm baffled. Homework Equations The Attempt at a Solution

$$ \int_0^{\pi}\frac{ad\theta}{a^2 + \sin^2\theta} = \int_0^{2\pi}\frac{ad\theta}{1 + 2a^2 - \cos\theta} = \frac{\pi}{\sqrt{1 + a^2}} $$ Consider $a > 0$ and $a < 0$ First I don't think the second part is correct. Shouldn't it be $1 + 2a^2 - \cos 2\theta$?

Hi, I know from basic math courses that inverse trig functions are multi valued (e.g. arctan(c)=θ+n*2∏). Now, if I solve a partial differential equation and I get an inverse trig function as part of my solution, does that mean solutions to the pde are non-unique? For example, if...

Homework Statement (tan/(1-cot))+(cot/(1-tan))=1+(sec)(csc) The Attempt at a Solution This problem showed up in my class as a warm-up, and when my teacher tried to solve it for us he got stuck. I've asked a few classmates in higher level math, and they all seem to get stuck. I...

Homework Statement Find the arc length of the curve r=4/θ, for ∏/2 ≤ θ ≤ ∏ Homework Equations L= ∫ ds = ∫ √(r^2 + (dr/dθ)^2) dθ The Attempt at a Solution After some calculations, and letting θ = tanx, I now have to find ∫ ((secx)^3/(tanx)^2). I am not sure how to do this, but i...

Homework Statement Use Euler's identity to prove that cos(u)cos(v)=(1/2)[cos(u-v)+cos(u+v)] and sin(u)cos(v)=(1/2)[sin(u+v)+sin(u-v)] Homework Equations eui=cos(u) + isin(u) e-ui=cos(u)-isin(u) The Attempt at a Solution I was able to this with other trig identities with no...

Homework Statement Given that cot \theta = -12/5 and csc \theta < 0, find sec\theta. This was a question on a test that I drew a blank on, and I'm still not sure how to handle it due to my "teacher" repeatedly dismissing me when I try asking about it. Now, it occurred to me that this could be...

Homework Statement \int\frac{dx}{x(x^{2}-1)^{3/2}} Homework Equations The Attempt at a Solution I know I need to use trig sub, but which form? I can't seem to find any that fit this form.

Need to find the angle at which a plane should aim if when traveling at 210km/h with a 40km wind east produces a resultant angle of 60 degrees. I can write that 60=tan^-1(210sin60/(210cos60+40) and proceed from there: tan60=210sinx/(210cosx+40) 1.73=210sinx/210cosx+40...

Homework Statement (3/5)cos2x + (3/5)sin2x The Attempt at a Solution I would think the answer would be 6/5, but it looks like the book is saying 3/5. I had a similar problem to this the other day and I tried finding it in my history but I couldn't.

I need to show that sin i*theta= i* sinh(theta). where sinh(theta) = .5[e^theta - e^(-theta)] and cos(theta) = .5[e^theta + e^(-theta)] and e^(i*theta) = cos(theta) + isin(theta) if I start with the formula sinh(theta) = .5[e^theta - e^(-theta)] and plug in e^(i*theta) = cos(theta) +...