What is Trig: Definition and 1000 Discussions

Homework Statement We have cosx = -7/9 in the third quadrant, and my question is how to find cos(x/2) and sin(x/2). I've tried using the sin^2x=1-cos2x/2 formula and its adjacent cosine formula. Is this the correct formula I should be using to get the answer for this question?

Homework Statement As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore. Homework Equations Sin θ Opp/...

My professor, when doing trig substitution in lecture, always defines theta between certain intervals and when he takes the square root, he adds an absolute value bar to the trig function and then makes sure its positive through the interval. For practical purposes, is it necessary to go through...

I have the expression sin^{-1}(cosx) I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help

Homework Statement Evaluate ∫(x^2-4)^(1/2) / x for x > 2 Homework Equations The Attempt at a Solution I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this...

\lim_{x\rightarrow \frac{\pi}{2}}\frac{\sin \left(x\cos x\right)}{\cos \left(x \sin x\right)} My Try:: \lim_{x\rightarrow \frac{\pi}{2}} \frac{\sin \left(x\cos x\right)}{x\cos x}.\frac{\frac{\pi}{2} - x\sin x}{\sin \left(\frac{\pi}{2} - x \sin x\right)}.\frac{x \cos x}{\frac{\pi}{2}-x \sin...

I've stumbled upon a system of equations that involves trig functions... 100cos(θ) + 200cos(ω) = 250 100sin(θ) + 200sin(ω) = 0 How do you go about solving a system like this? It's nonlinear, so linear algebra won't work...

Homework Statement Find the Maclaurin series for (tanx)2 Homework Equations f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2}+... The Attempt at a Solution I don't see how it's reasonable to do this problem without using a computer. The derivative of (tanx)2 is 2tanxsec2x, then the...

Find the exact value of \sin \frac{\pi}{180}.

Homework Statement Simplify: (sin t + cos t)2 / sin t cos t Homework Equations tan t = sin t/cos t cot t = cos t/sin t cot t = 1/tan t The Attempt at a Solution (sin t + cos t)2 / sin t cos tsin2 t + 2sin t cos t + cos2 t / sin t cos t(sin t/cos t) + 2 + (cos t/sin t) tan t + cot t + 2...

Homework Statement y = (4/3)cos(x/2 + pi/6) - (2/3) (0 <= x < 2pi) Find the maximum and minimum values for the trigonometry function without calculus or drawing the graph. Basically in the solution they apply the transformations to the domain given in order to find a new domain...

The problem gave that: theta= arcsin(-5/8) It wants us to find the other five trig function values. In order to do that, I turned the original function to sin(theta)= - 5/8 From there I was able to find csc(theta) to be -8/5. Using the pythagorian theorem I found the other side...

Hello, In a trig verbiage such as "if cos t = -8/17 and pi/2 <t <pi" could someone please provide an alternate way of interpreting "and pi/2 <1 <pi"? I don't understand what is trying to be said with this portion. Any alternate interpretations would be wonderful. Thank you for your...

Homework Statement tanx-1 = cos2x The Attempt at a Solution I know tanx = sinx/cosx but I don't know which identity to pick for cos2x

33. find two values of $\theta$ , $0^{\circ} <\theta<360^{\circ}$ that satisfy the given trigonometric equation. without using calculator. a. $\displaystyle \sin\theta=\frac{1}{2}$ b. $\displaystyle \cos\theta=-\frac{\sqrt{3}}{2}$ c. $\displaystyle \csc\theta=-\sqrt{2}$

I have a question regarding what I highlighted in the paint doc. How can they assume that the function is increasing? As a matter of fact its not increasing on the entire interval from 0 to pi.

Homework Statement integral of sqrt(x^2-36)/x) Homework Equations sqrt(x^2-a^2) = asec(u) Pythagorean identity The Attempt at a Solution I used trig sub on the x^2-36 and changed that to x=36sec(u) and dx= 36sec(u)tan(u). I simplified the square root in the numerator using...

Hi I just found out that cos(z) and sin(z) are unbounded and tend to ∞ which I find strange ! But the part I'm struggling with is that I can't reconcile that fact with the fact that they both have a period of 2pi. Surely that means that each value in the range 0-2pi is repeated in the range...

Homework Statement prove that (sinA +sin3A + sin5A)/(cosA + cos3A + cos5A) = tan3A Homework Equations sinP + sinQ = 2sin((P+Q)/2)cos((P-Q)/2) cosP + cosQ = 2cos((P+Q)/2)cos((P-Q)/2) The Attempt at a Solution (sin3A + sinA) + sin5A = 2sin2AcosA + 2sin((5/2)A)cos((5/2)A) (cos3A +...

Homework Statement What value(s) of θ will result in the block being accelerated 9.0m/s2 to the right? Homework Equations ƩFx = max N = mg - P sin(θ) The Attempt at a Solution P cos(θ) - μkN = max P cos(θ) - μk(mg - P sin(θ)) = max P cos(θ) + μk P sin(θ) = max + μkmg cos(θ) +...

I was having some free time and decided to do some mathematics from my high school mathematics book.These two problems remained, and I am completely clueless to the solution approach. Homework Statement A. If sin(θ)-cos(θ)=1, prove that sin(θ)+cos(θ)=±1 B. If tan(θ)+sec(θ)=10, prove that...

Forum, do you have any idea how to solve the trigonometric inequality \cos (x) < \sin (x) strictly algebraically? The conventional(?) approach is to first solve \cos(x) = \sin(x) and then draw the graphs for each function in order to find the correct interval. However, I would love to know if...

what method should i use here(except integration by parts)? \begin{align*}\displaystyle \int sec^3\theta \,d\theta\end{align*}

I am new to Mathematica and I'm not sure if I'm using it properly but sometimes the output doesn't make sense to me. I Hope someone can help me understand or correct my usage. When solving trig equations Mathematica's Solve[] function gives the correct list of solutions but some of the...

I'm having some confusion with a couple trig identities. On wikipedia (http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities), the following two identities are listed: sinθcosβ = (1/2)[sin(θ+β) + sin(θ-β)] and sinβcosθ =...

0. The app does not have the template built in so ill do my best, sorry i don't have a computer right now. 1. This is a personal project, and there is a lot to it but I'm cutting out down to where i need help. Imagine a 2x2 grid of squares (2d for now). The center vector is at (0,0), and the...

Homework Statement find the values of x between 0 and 360 sin2x + cosx = 0 Homework Equations The Attempt at a Solution sin2x + cosx = 0 2sinxcosx = -cosx 2sinx = -1 sinx = -1/2 x = 210, 330 I'm guessing I lost the other solutions when I divided cosx by itself

please correct me with my solution here. ∫cos72xdx = ∫(cos62x cos2x)dx =∫(1-sin22x)3cos2x let u = sin2x; du = cos2xdx dx = (du/2cos2x) ∫(1-u2)3cos2x*du/2cos2x 1/2∫(1-u2)3*du 1/2∫(1-u2)2*(1-u2)du 1/2∫[(1-3u2-u4-u6]du 1/2∫du-3/2∫u2du-1/2∫u4du-1/2∫u6du...

I can find for example Tan(2x) by using Euler's formula for example Let the complex number Z be equal to 1 + itan(x) Then if I calculate Z2 which is equal to 1 + itan(2x) I can find the identity for tan(2x) by the following... Z2 =(Z)2 = (1 + itan(x))2 = 1 + (2i)tan(x) -tan(x)2 = 1...

How about these? ∫tan^3xdx ∫(sin^4x cos^2x)dx

Homework Statement Prove that the two trig identities are equivalent. cos \ x \ -\frac{cos \ x}{1-tan \ x} \ = \ \frac{sin \ x \ cos \ x \ }{sin \ x \ - \ cos \ x} The Attempt at a Solution My professor recommended that we only work with one side of the equality when we're trying...

I have no idea how to solve these. please help. ∫(sinx/1+sinx)dx ∫(sin^2x cos^2x)dx

I am trying to resolve a trig identity for some notes I am typing up. On paper, I wrote recall $e(\sin(E_1) - \sin(E_0)) = 2\cos(\zeta)\sin(E_m)$. I have no idea what I am recalling this from now at least. Identities I have set up are: \begin{align} E_p &= \frac{1}{2}(E_1 + E_2)\\ E_m &=...

Homework Statement I was just curious about something involving trig. How can sintheta <= 1. Shouldnt it be just sintheta < 1. By saying that its less or EQUAL to 1 does that not mean that the hypontenuse and the opposite side are equal, but the hypotenuse always has to be the longest side...

How?? Which Trig Identityis that? Homework Statement Homework Equations The Attempt at a Solution sin^2 = 1- cos^2 ??

Can't figure out how they're constructed. I'm guessing it would be geometric in nature. It would be nice to be able to derive at least a few of the ones I inevitably forget through disuse. Math level: ordinary differential equations.

Hey guys,I need some help on the following trig identities: 1) sin2x = 2tanx/1+tan^2x 2) sin2x/sinx - cos2x/cosx = secx My attempts: 1) LS: sin2x 2sinxcosx 2sinx/cosx 2tanx/1+tanx Not sure if this is right or not. I kind of understand my third step but it just doesn't seem...

Quick question guys.. I understand how trig graphs work (cos, sin, tan etc.). What I don't understand is when there is a horizontal translation of say, pi/4, I notice that the graph moves, but I don't really understand how to know exactly how far to move. For example if your HT was pi/4 and...

1. Does the limit exist of the following: lim as x→ 1- ((cos^-1(x))/(1-x)) 2. Homework Equations : 3. The Attempt at a Solution : lim as x→ 1- ((cos^-1(x))/(1-x)) = lim as x→ 1- (cos^-1(x))/ lim as x→ 1-(1-x) Let y = 1-x lim as y→0 (cos^-1(1-y)) / lim as y→0 (y) =...

Homework Statement Prove the following identities 31c) sin(\frac{\pi}{2}+x)=cosxHomework Equations sin2x+cos2x=1 The Attempt at a Solution The idea here is to prove the identity by making LS=RS so here is what i have done, but I am not sure if it is the right way, since the book shows it...

I have dabbled in trig doing physics and understand enough to do simple problems with the 6 trig functions but next spring ill be taking trig and I am wanting to get a good self teaching book. does anyone have any suggestions for one. I would like to get one that has at least plenty of examples...

I'm working with the integral from 0 to infinity of t^(x-1)e^(-atcos(b))cos(atsin(b)) with respect to t. specifically, I'm asked to solve in terms of the gamma function. my question is more of what general technique i should use. all I've been able to do so far is beat it to death using...

Hello there, I have a problem I'm hoping someone can help me with. I'm writing a bit of code for computing the value of pi that converges faster than a previous piece that relies on the leibniz series. Anyway, I'm struggling with showing how this identity arises. tan(2t) = 2 * tan(t) / 1 -...

Homework Statement This isn't really a homework question, just working through Rudin and got caught up on something. C(x) and S(x) refer to cos(x) and sin(x) respectively. Here is the section in question: http://grab.by/mSo8 Homework Equations The Attempt at a Solution Well the part I'm...

Homework Statement Hello, I am in differential equations currently and I have a homework question regarding simplifying sin( Pi t)/4 into .5 * i E^(-.25 i pi t) - .5 * i E^(.25 i pi t) Homework Equations I think they might be using Euler's Identity, but I am unsure. E^(a +...

Given: A + B + C = 180 degrees Prove: TanA + TanB + TanC = TanA x TanB x TanC First time submitting something. Thank you all.

Homework Statement Integrate the following using substitution techniques ∫e3tcsc(e3t)cot(e3t) dt Homework Equations csc(t) = 1/sin(t) cot(t) = 1/tan(t) cot(t) = cos(t)/sin(t) 1 + cot2(t) = csc2(t) The Attempt at a Solution ∫e3tcsc(e3t)cot(e3t) dt set u = cot(e3t)...

Homework Statement A rocket is moving into the air with a height function given by h(t) = 200t^2. A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after liftoff? Homework...

I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?

This isn't homework, It is just book problems that I am practicing, I am checking some answers with wolfram and others with the book answers. Homework Statement \begin{align} \int \frac{sin(w)\,dw}{\sqrt{1-cos(w)}}\\ \end{align} Homework Equations I used u substitution... Not sure if I...