What is Tan: Definition and 152 Discussions

Tantalum nitride (TaN) is a chemical compound, a nitride of tantalum. There are multiple phases of compounds, stoichimetrically from Ta2N to Ta3N5, including TaN.
As a thin film TaN find use as a diffusion barrier and insulating layer between copper interconnects in the back end of line of computer chips. Tantalum nitrides are also used in thin film resistors.

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  1. W

    Find sin, cos, and tan for a given quadrant angle

    Find (a) sin ∅, (b) cos ∅, and (c) tan ∅ for the given quadrantal angle. If the value is undefined, write “undefined.” My quadrantal angle is -450° Sin = opp/hyp Cos= adj/hyp Tan= opp/adj I drew a graph and put the angle -450° in the 3rd quadrant because both x and y are negative and I...
  2. T

    Question of the basic properties of tan

    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...
  3. D

    When tan theta is -ve why did we assume that it's in the second quad?

    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...
  4. N

    Finding the range of values for tan theta > 1

    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...
  5. W

    How can the Power Series for Arc Tan be Proven for Homework?

    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}
  6. U

    Trig, find tan A and tan B (no numbers given)

    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}...
  7. P

    Complex Algebra: Trigonometry (tan)

    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...
  8. U

    Expressing tan θ in a triangle

    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...
  9. D

    Finding 10 Positive Solutions for Tan x = 1/x Numerically

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

    (1 + cot + tan )(sin - cos ) whole upon sin^3 - cosec^3

    (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 :/
  11. C

    Partial Differentiation of Inverse Tangent Function

    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...
  12. C

    What is the Derivative of x / (2 - tan x)?

    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...
  13. baby_1

    How can I solve for u and ultimately find ω in this equation?

    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.
  14. M

    If tan x = k(where k is a positive constant),How is tan( pie/2 − x)=1/k

    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...
  15. L

    Find the function of the form y = tan kx

    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...
  16. C

    Hence express tan (pi/12) in surd form.

    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)...
  17. S

    Question about tan, cos, and sin

    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...
  18. A

    Strategies for Solving Integrals Involving Trigonometric Functions

    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}+...
  19. D

    MHB Integrating $\tan z$ Around a Circle of Radius 8

    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?
  20. U

    Identities sin, cos, tan etc. stuff

    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
  21. M

    MHB How to Simplify an Integral Involving tan x

    $ \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
  22. A

    Solving SIN, COS, TAN with a TI-30XA Calculator

    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...
  23. N

    If f(a)=g(a) and f(b)-g(b), prove they will have parallel tan lines

    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...
  24. N

    If f(a)=g(a) and f(b)-g(b), prove they will have parallel tan lines

    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...
  25. F

    Finding the nontrivial zeros of Tan x = x

    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...
  26. H

    Calculating Missing Angles and Sides in Right Triangle Using Trigonometry

    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...
  27. H

    How to use arc tan to find an angle?

    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
  28. J

    Find Limit of (tan x)^(tan 2x) as x approaches pi/4 | Tan() Homework

    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...
  29. C

    Horrible expression involving logs and inverse tan functions

    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...
  30. N

    Need help with determing domains of sin, cos, and tan

    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)...
  31. QuarkCharmer

    Finding tan line to curve via implicit dif.

    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...
  32. C

    How Does Quadrant Affect Values in Trigonometric Functions?

    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?
  33. K

    Hard hyperbolic tan integral :/

    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...
  34. T

    Is Tan-1z Analytic Throughout the Complex Plane?

    The function Tan-1z is defined by: Tan^{-1}z=\int_0^z \frac{dt}{1+t^2} where the path of integration is a straight line. For what region of the complex plane is Tan-1z analytic? I'm not too sure about this. I can see that the integrand is analytic everywhere except at t=+i and t=-i so...
  35. B

    Use de moivres theorem to show that tan 3theta=something

    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...
  36. B

    Can someone explain this inverse tan integral for me please?

    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.
  37. M

    Unpacking Trig Ratios: Understanding Sine, Cosine, Tan, and More

    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
  38. Darth Frodo

    2nd Level Vectors question. Tan ratios.

    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...
  39. P

    How Is the Tan Power Series Derived Using Sin, Cos, and Bernoulli Numbers?

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

    What Is the Solution for x in the Equation tan((πx)/2) = √(3)/2?

    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
  41. A

    Exploring the Possibility of a Cosmic Tan

    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...
  42. K

    Trigonometric identity for inverse tan

    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 -...
  43. r-soy

    I want help to find tan of polar correctly

    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...
  44. R

    Find values of sin, cos, tan, sec, csc, and cot without a calculator

    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...
  45. J

    Understanding the Relationship between Negative Angles and Tangent Function

    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...
  46. J

    How Do I Choose Between Sin, Cos, and Tan in Trigonometry Problems?

    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...
  47. Q

    Solving tan x = x: A Numerical Method

    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!
  48. A

    Inverse Laplace Transformation of Inverse Tan function

    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...
  49. N

    How do you tell if tan x=0.5371, is in radian or degree?

    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
  50. S

    What is the meaning of the sum of tan A and rad A?

    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...
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