Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.

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1
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1answer
82 views

NIntegrate gives two results for two forms of the same function. Which one to trust?

I am interested in evaluation the following integral numerically (since apparently there is no analytical solution) $$\int dx \,x^3 \left(e^{2 i c x }-i \text{erfi}\left(\frac{x +i c ...
0
votes
0answers
4 views

tan(arcsin x) if x>0 [migrated]

I drew a triangle with 1 as the hypotenuse and x as the side opposite of sine. I'm getting a blank on how to get the bottom part of the triangle. Would the bottom side just be cos theta? ie. tan theta ...
0
votes
1answer
65 views

Calculating the angle between the line joining two points and the x-axis [closed]

I need to calculate the angle between two points, the returned result should between $0$ to $2π$ and getAngle[point1, point2]==getAngle[point2, point1]. I have ...
0
votes
0answers
12 views

Trilateration Using TDOA [migrated]

I am having some trouble to find or implement an algorithm to find a signal source. The objective of my work is to find the sound emitter position. To accomplish this I am using three vibration ...
-1
votes
1answer
26 views

What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
0
votes
2answers
54 views

Put a trigonometric equation in the form A*cos(theta)+B*sin(theta)+C=0 [closed]

eq = (Cos[Θ[t]]cf - Cos[γ1[t]] mf + Cos[γ2[t]] mf)^2/cf^2 + (Sin[Θ[t]]cf + Sin[γ1[t]] mf - Sin[γ2[t]] mf + xP1[t] - xP2[t])^2/cf^2 Can you help me to simplify and ...
0
votes
1answer
34 views

Replacement of a group of variables in trigonometric expression

I would like to make simplification of trigonometric expressions by using a replacement a group of variables. Here the equation I have to simplify : ...
3
votes
1answer
54 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
0
votes
1answer
48 views

How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?

I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write $$ ...
1
vote
1answer
72 views

Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2 $$ Here $z$ is the complex ...
3
votes
1answer
92 views

Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
1
vote
0answers
28 views

How can PowerExpand be made to evaluate the ArcTan form that takes two arguments?

Consider c = Cos[phi]; s = Sin[phi]; ArcTan[c, s] // PowerExpand ArcTan[s/c] // PowerExpand which yields ...
4
votes
1answer
79 views

Simplify $\tan(\arctan(a) - \arctan(b))$

I want to simplify the expression $\tan(\arctan(a) - \arctan(b))$ to $\tfrac{a-b}{1+a\cdot b}$ (if $b \neq - \tfrac{1}{a}$). Right now, the output of ...
4
votes
0answers
64 views

Why does Mathematica gives a solution which is not in the domain of the cot function? [closed]

I've tried to solve the equation $\cot \theta = 2 \cot 2\theta$ with the command Reduce and Mathematica gave $\theta = n\pi$ as solution, with $n$ an integer. But ...
0
votes
1answer
48 views

Quick simplification of a fraction of 2 trigonometric equations

I would like to simplify a fraction of 2 trigonometric functions ...
1
vote
1answer
84 views

Solving trigonometric functions in Mathematica

I am new to Mathematica language and recently I had the need to solve the following equations with two variables, A and B: ...
2
votes
1answer
72 views

How to a convert a 2D vector into an angle [closed]

How do you calculate the angle between the line from the origin to a point $(x,y)$ and the horizontal axis?
2
votes
1answer
90 views

What function can transform A*Cos[x]+B*Sin[x] to Q*Sin[x+R] form? [duplicate]

I've tried several functions related to trigonometric transformations, namely TrigFactor, TrigExpand, ...
1
vote
1answer
54 views

Solving a simple trigonometric equation in a range

I would like to solve a simple trigonometric equation, for example $\sin\theta=\frac{1}{2},$ but Solve gives the single solution obtained by using the inverse ...
8
votes
1answer
192 views

How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
1
vote
1answer
59 views

3D-plots of Complex-parametered trig-functions returns empty plot

I first tried to plot a parametric equation as follows; ...
4
votes
1answer
70 views

Strange behavior of ArcTan [duplicate]

I've noticed a strange behavior of Mathematica's ArcTan function with two arguments. If both arguments are 0 or ...
3
votes
0answers
88 views

Inconsistent results for symbolic trigonometric integral

I am trying to evaluate (on Mathematica v.9) the integral \begin{equation} \int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y, \end{equation} where $t$ is an even, positive integer. ...
-2
votes
1answer
83 views

Simplify a expression with cos 2x

I would like to simplify the following expression : r Cos[γ[t]] + Sqrt[l^2 - r^2/2 + 1/2 r^2 Cos[2 γ[t]]] by using the mathematical expression : ...
1
vote
0answers
31 views

Not reducing Trig Functions to zero [duplicate]

How do I tell Mathematica to reduce trig functions to zero when their arguments are integer multiples of pi or 2pi? I have this: ...
6
votes
3answers
864 views

Replacing Tan[x] with Sin[x]/Cos[x]

Why doesn't this work? (1 - Tan[x])/(Sin[x] - Cos[x]) /. Tan[x] -> Sin[x]/Cos[x] I get back: ...
0
votes
1answer
43 views

Solving a trigonometric equation for all $x$ using constant coefficients

I want to find the coefficients $a$, $b$, $c$, etc. that make an equation like $a+bx=x$ true for all $x$, but for trigonometric functions of $x$. For example ...
1
vote
3answers
113 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
2
votes
1answer
102 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
1
vote
0answers
48 views

Write trigs in terms of Cosine only

I have a long expression having terms that go in squares like Sin[x]^2 and Sin[x/2]^2 and so on... I would like to rewrite my ...
3
votes
3answers
210 views

How can I make Mathematica trigger the simplification of ArcCos[a]+ArcCos[b]?

According to this Wikipedia subsection my guess is that I should be able to convince Mathematica to return zero when doing ...
2
votes
3answers
116 views

Adding more specific assumptions to Integrate

Let's say I would like to find a symbolic form for the integral $$\int_0^{2\pi}\sin^nx\,\mathrm{d}x$$with the added condition that $n$ is not only an integer, but an even one at that. Can this be ...
0
votes
1answer
174 views

Why does Mathematica give this ArcSin[2] result?

The code N[ArcSin[2]] evaluates to 1.5708 − 1.31696 I but it should be undefined instead because it is on the branch ...
0
votes
1answer
53 views

Using Trig functions

This is a fairly simple notation problem. I am trying to compute ArcTan of the point (5,2). I have the code: ArcTan[5,2] which outputs: ...
8
votes
2answers
127 views

Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. ...
0
votes
1answer
73 views

Reducing solutions of Sin[2t] Sin[t] == Cos[t] to a simpler form [closed]

I evaluated Solve[Sin[2 t] Sin[t] == Cos[t] && 0 <= t < 2 Pi, t] And got these results. ...
2
votes
1answer
51 views

TrigExpand-ing too far

Something simple: I'd like TrigExpand[Sin[3n-3]] to return Sin[3n]Cos[3]-Cos[3n]Sin[3] instead of ...
1
vote
2answers
168 views

Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
1
vote
1answer
207 views

How to solve trigonometric equations

I have the following problem: I need to solve the equation: $$\frac{\cos\left(x\right)}{x^6} - \frac{6 \sin\left(x\right)}{x^7}==0$$ and I don't really remember how to do it symbolically. Some help ...
0
votes
1answer
38 views

Shade where a function f lies below a function g [duplicate]

I have two functions: f[x_] = 2 Cos[x] g[x_] = -Sqrt[3] I find the points of intersection. ...
3
votes
1answer
159 views

Sum to Product Trig Identities

All, I was enjoying sum to product trig identities in Mathematica, smiling that it was going well, producing the same answers trig students get by hand. ...
0
votes
1answer
95 views

Find tangent of alpha/2 given cos(alpha)=-3/5, where pi<alpha<3pi/2 [closed]

What would be folks' favorite way of finding $\tan(\alpha/2)$, given $\cos\alpha=-3/5$, where $\pi<\alpha<3\pi/2$?
1
vote
0answers
49 views

Tangent of 2 times arc cosine of -3/4 [closed]

Tan[ArcCos[-3/4] Returns the exact answer: -(Sqrt[7]/3) But: Tan[2 ArcCos[-3/4]] Does not return an exact answer. Any way ...
1
vote
3answers
361 views

Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to ...
2
votes
1answer
98 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
1
vote
1answer
51 views

find the inverse of a hyperbolic function

Hi everyone I am new in Mathematica and I am trying to find the inverse of a function which contains hyperbolic tangents and I hope someone can help me. The function is y=(a)tanh(d(x-g))+ ...
0
votes
2answers
108 views

Find *all* numerical solutions to cosine based equality

To help with http://astronomy.stackexchange.com/questions/11456/ I'm trying to find all numerical solutions to: 5.20427*Sin[0.529699*t] == Sin[2*Pi*t] Since the period of the first function is ...
5
votes
3answers
989 views

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
0
votes
1answer
49 views

Expanding a function with trigonometric expressions in a controlled manner by excluding addition identities

I want to simplify a nonlinear equation with trigonometric terms. After I've expanded I don't want to loose open terms to Trigonometric Addition Formulas ...
6
votes
1answer
193 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...