Tan Definition and 149 Threads

Homework Statement I've solved a problem in my engineering homework to a point where I have the following data: ψ = arctan(3) = 71.57 (degrees) , inverse tangent of 3 δ = 30 degrees solve for gamma and chi (χ): tan(2gamma) = tan(2ψ)cos(δ) sin(2χ) = sin(2ψ)sin(δ) Homework Equations...

The problem says " Two forces of magnitudes 12 and 15 Newton are applied to a point and the tangesnt of the angle between them is -3/4. Find the resultant of the two forces and the measure of its angle of inclination on the first force. In the answer it says that the theta belongs to the...

Homework Statement How to find the values of theta that make tan theta > 1 true? The Attempt at a Solution From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to...

Homework Statement Prove. Homework Equations arctan(x) = x - \displaystyle \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} for -1 < x < 1. The Attempt at a Solution \displaystyle \sum^{∞}_{n=1} \frac{x^{n+2}}{n+2}

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}...

Homework Statement Let tan(q) with q ε ℂ be defined as the natural extension of tan(x) for real values Find all the values in the complex plane for which |tan(q)| = ∞ Homework Equations Expressing tan(q) as complex exponentials: (e^iq - e^(-iq))/i(e^iq + e^(-iq)) The Attempt...

Homework Statement The original question is from AP French's Classical Mechanics. It's about a boat trying to catch up with a ship. I've interpreted the question as follows: which is to express tan θ as a function of u and v. I tried working with vectors, where v is actually -v in...

How do I find the first 10 positive solutions numerically? $$ \tan x = \frac{1}{x} $$

(1 + cot + tan )(sin - cos ) whole upon sin^3 - cosec^3 = sin^2cos^2 prove this . ( assume theta is front of all functions ) , i don't know where to start :/

Homework Statement find dz/dy(partial) z= tan-1(y/x) Homework Equations The Attempt at a Solution z= tan-1(y/x)let u=y/x z= tan-1(u) dz/du = 1/ (1+u2) so dz/dy = dz/du (du/dy) du/dy = 1/x so dz/dy = (1/1+u2)(1/x) = 1/ 1+ (y2/x2) * 1/x = 1/ x + (y2/x2)x) = x / x + y2but I should be...

Homework Statement I need to find the derivative of x / (2 - tan x). Homework Equations I do everything Wolfram Alpha does here: http://www.wolframalpha.com/input/?i=derivative+x+%2F+%282+-+tan+x%29 Except I don't understand why the answer is (2+x sec^2(x)-tan(x))/(-2+tan(x))^2. I...

Hello Could you help me to solve this problem? i want to find w asnwer is 151660 but i want to know the approach to solve it.

Homework Statement The exact question is in question one part ii of http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_s10_qp_11.pdfHomework Equations The Attempt at a Solution For the first one I just pluged in a value for x, and...

Homework Statement Find the function of the form y = tan kx that pass through (290 degrees, -1)Homework Equations y = tan kx The Attempt at a Solution y = tan kx -1 = tan k(290 degrees) arctan(-1) = k290 degrees -pi/4 = K 290 I don't know where to go from here, or even if this is...

Homework Statement Let z= √3 -i and w= 1+i i)calculate zw in "a+ib"form ii)Write z and w in polar form and thus write zw in polar form iii)Hence express tan (pi/12) in surd form. Homework Equations The Attempt at a Solution (√3 -i)(1+i) = (√3+1)+(√3i-i)...

So, I am trying to understand what tangent, cosine, and sine are in practical terms e.g. if something is tangent with something else we know it is touching that something. That seems like a practical definition of tangent to me. So, then what is a sine? what is cosine? I was thinking like...

Hello. I was trying to solve Lagrangian equation and I manage to reduce second order differential equation that I got: \ddot{\varphi}+\alpha\frac{tan\varphi}{cos^{2}\varphi}=0; where \alpha is a constant, to first order differential equation: \dot{\varphi}^{2}+...

So if I wanted to integrate $\tan z$ around a circle of radius 8, I would need to identify all the singularities and then use $$ \int_Cf=2\pi i\sum_{n = 1}^m a_i\text{Res}_{z_i}f, $$ where $a_i = \eta(\gamma,z_i)$ the winding number. Correct?

Homework Statement ((cos x)/(1+sin x))+((1+sin x)/(cos x)) Homework EquationsThe Attempt at a Solution multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x) get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x) and I have no idea where to go from here

$ \displaystyle \int_{0}^{\pi/2} \frac{dx}{1+(tan(x))^{\sqrt2}}$ Could anyone tell me how to start, In a book ,it was given that $\sqrt2$ does not even matter

Hello, I'm having some problems. So for geometry class today, the teacher taught us this COS, SIN, TAN stuff. I got the concept how to get the fractions from the triangle and everything. Problem is how to plug it in the calculator. I have a basic TI-30XA, and I'm trying to plug in fractions...

1. Homework Statement (a) If f and g are differentiable functions on the interval [a,b] with f(a)=g(a) and f(b)=g(b), prove that at some point in the interval [a,b], f and g have parallel tangent lines. (b) Prove that the result of part a holds if the assumptions f(a)=g(a) and f(b)=g(b) are...

Homework Statement (a) If f and g are differentiable functions on the interval [a,b] with f(a)=g(a) and f(b)=g(b), prove that at some point in the interval [a,b], f and g have parallel tangent lines. (b) Prove that the result of part a holds if the assumptions f(a)=g(a) and f(b)=g(b) are...

I can do the first part no problem. I then drew the graph, am I right in saying there is an infinite sequence because the lines intersect an infinite amount of times, because tan is periodic and has vertical asymptotes? I have no idea about showing why the first non rivial zero is bounded like...

Homework Statement Ok, so this is really basic and i could do it at the snap of a finger liek a year ago but it's completely escaped me. Maths is too much. This is a right angle triangle, with the right angle on angle C. Angles are marked A, B and C. Side CB = Adjacent, Side BA = Hyp and...

in physics we were doing a problem that essentially involved vectors and in the end we were left with 2 displacements. how would i find the angle between them if it was not a right triangle? i asked someone and they said that i could find it using artan(Ry/Rx) ...R being one of the displacements

Homework Statement \displaystyle \lim_{x\rightarrow \frac{\pi}{4}}\left(\tan x\right)^{\tan 2x} Homework Equations The Attempt at a Solution let \frac{\pi}{4}-x = t\Leftrightarrow x=\frac{\pi}{4}-t and t\rightarrow 0 \lim_{t\rightarrow 0}\left(\tan...

Homework Statement \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0 Homework Equations \frac{dy}{dx} + (y^4-1) = 0 The Attempt at a Solution \frac{dy}{dx} = (1- y^4) \frac{dy}{1- y^4} = dx Then I get a horrible expression involving logs and inverse tan functions...

Homework Statement Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses. i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)...

Homework Statement Stewart Calculus (6E) 3.6 question #26 Using implicit differentiation, find the equation of a tangent line to the curve at the given point. x^2+2xy-y^2+x=2 Through point p(1,2) I just want to know if I am doing this correctly. Homework Equations The Attempt at a Solution...

How would I find cos for tan when.. Tan b = (-√3) Theta lies in quadrant iii Sin b would equal (-√3) / 2 So Cos b would equal -1 / 2?

Homework Statement tanh{[(2 *g*t)/(c)]+[(2*g*exp(-rt))/(r*c)]-[(2*)/(r*c)]} in terms of t Homework Equations when I plug into maple I get -(1/4)*c*ln(tanh(2*g*(t+1/r(e^(-rt))-1/r)/c)-1)/g-(1/4)*c*ln(tanh(2*g*(t+1/r(e^(-rt))-1/r)/c)+1)/g The Attempt at a Solution This cannot be...

Homework Statement use de moivres theorem to show that tan 3theta=(3tan theta -tan^3 theta)/(1-3tan^2 theta) Homework Equations The Attempt at a Solution tan 3theta=sin3theta/cos3theta =(3sin theta - 4 sin^3theta)/(4cos^3theta -3cos theta) so then i divided everything by...

integral of (Ldv)/(AgL+v^2) from [v0,0] I'm supposed to get (...)arctan(...) where (...) are 2 different quantities. I'm confused on how to get arctan out of this integral whenarctan = integral of (1*dv)/(1+v^2) from [0,x] Help is appreciated.

Homework Statement What is the importance of knowing how to express trig ratios in terms of sine, cosine, tan, cosec, sec, or cot? Homework Equations The Attempt at a Solution

If I am only ginen the following how can I solve the whole Tan ratio part? If vector U is 10 units "Alpha Symbol" = Tan -1 (Tan inverse) 3/4 find U Vectors V = 13 units "Beta" = Tan -1 (Tan inverse) 3/4 find V I tried to multiply the 2 Tan ratios together but no luck. I imagine you...

How can the tan power series be derived from the sin and cos power series? Where do the Bernoulli numbers come in?

Homework Statement tan((π(x))/2) = √(3)/2 Homework Equations The Attempt at a Solution tan(x) = √(3)/2 x= π/6 + πn, since Tan has a period of π This is where I'm stuck

Hi. If there were a whole line of bright lights strung from one side of the universe to the other, and i set off from one side to the other at sufficient speed, would the doppler shifiting mean that i could get a sun tan from the lamps that otherwise emit standard light that might be used to...

Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...

Hi I face some problem when i try to find tan in like this questions for example : write in polar z1 = 1 - i the answer is -5π/4 but my answer is tan Q = y/x = -1/1 = -1 how I get -5π/4 -------------- ex : 2 z = -root3 + i my answer...

Homework Statement I'm wondering how you would find values of sin, cos, tan, sec, csc, and cot without a calculator. I don't have a specific problem but how would you solve things like tan 45 degrees, sec 30 degrees, and cos -30 degrees? 2. Relevant info I have the values of sin and...

This isn't my problem, it's a friends. I'll post my explanation and you tell me what's wrong with it cause she still doesn't understand. Thanks. http://img43.imageshack.us/img43/3020/32112328.png Find tan(theta), given the coordinates of the arrow. I said "well tanx = tan(x-180) by...

No problem specifically, just more of a method question. I am extremely confused on when to use sin cos and tan. Say for instance it gives me an angle, say theta, and one side. How would I be able to tell what to use sin cos or tan. I know the trick SohCahToa but I really am confused. I am in a...

Homework Statement tan x = x Homework Equations The Attempt at a Solution how do i solve this equation without using graphs? is there a numerical method ? thanks a lot!

Homework Statement Take the Inverse Laplace Transform of F(s) where F(s)=((s)(tan-1(1/s))) Homework Equations The Attempt at a Solution i know that f(t)=L-1(F(s))=(-1/t)L-1(F'(s)) and d/ds(1/tan-1(x))=1/x^2 +1 but the example I'm given with an inverse laplace of tan-1 is way...

Homework Statement How do you tell if tan x=0.5371, (0.5371)is in radian or degree? (0\leqx\leq2\pi)thanks Homework Equations The Attempt at a Solution

Today I was doing a homework that asked me to calculate the sum of some particular tangential acceleration and radial acceleration in a circular motion. We all know clearly about the concepts independently, but I wonder what the physical meaning the sum of the two accelerations is? Or it is...

What criteria decides whether a trig function is an odd or even?

cos and sin are periodic at 2pi How about tan?