# Questions tagged [trigonometry]

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

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### Collect the coefficients through the Cos argument

I have for example the following expression: ...
66 views

### Slow integration of trigonometric expression speeds up after TrigReduce

I'm trying to integrate a trigonometric expression as Integrate[Cos[2 t] Cos[3 t] Cos[4 t] Cos[5 t] Sin[2 t] Sin[3 t], {t, 0, 2 Pi}] The final results is correct (...
1 vote
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### Simplification of long trigonometric expression taking a long time

I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
80 views

### How to do some trigonometric derivations

Two substitutions fail, so do I forget some earlier steps? For Cos[x] == Sin[(1/2)*Pi + x] /. x -> (1/2)*x = true I don't get the final answer, but only true. <...
593 views

### Finding which given functions are equal to each others

I have about 50 piece functions (generally trigonometric functions). I want to find out which ones are equal to each other after some simplifications such as ...
106 views

### Solving a set of trig inequalities

I have a set of inequalities Cos[a]Cos[b]>=Cos[t-a]Cos[b]&&Cos[a]Cos[b]>=Cos[t/2]&&Cos[a]Cos[b]>=Sin[t/2]&&a<=t<=Pi How to ...
130 views

### Mathematica vs Rubi --- integrate $f(x,y) = x \sin^2 x + a x y$ --- Mathematica got this round? [closed]

Consider the function: $$\begin{equation} f(x,y) = x \sin^2 x + a x y \end{equation}$$ with $a$ being a constant. We want to do the indefinite integral over $x$ and then over $y$. We do that using <...
1 vote
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### How to sort out only terms that relates to certain variable in the results of TrigReduce? [closed]

I have a large function $F(\theta,\alpha_1,\alpha_2,...)$ which involves only trigonometric polynomial of these angles. I want to calculate $\frac{1}{2\pi}\int_0^{2\pi} Fd\theta$, but the function is ...
485 views

### How do you make Tan[A+B] expansion give the well known high school answer? [duplicate]

What command makes Tan[A+B] expand to (Tan[A]+Tan[B])/(1-Tan[A]Tan[B])? TrigExpand does not ...
94 views

### Strange effect in the SphericalPlot3D [closed]

I found something odd in Mathematica when using the SphericalPlot3D command. Ranges for $x,y∈[0,2 \pi]$ are the same. All I do is swap sine and cosine. But when I ...
1 vote
141 views

### How can I get mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$?

How can I get Mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$ (1)? ...
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### Updating the association with answers from the TrigProperties Function

I have created a list of rules I would like to update with values. My goal here is to be able to write the following: ...
64 views

### NIntegrate giving different results after a change of variables

When I compute numerically the following double integral: \begin{equation} f(x,y)=\int_{-\infty}^{+\infty}da\int_{-\infty}^{+\infty}db\, \cosh\left[\frac{\sinh^{-1}(a)-\sinh^{-1}(b)}{2}\right]\, \exp\...
88 views

### Calculate ArcTan in AceGen

I am working on a material model SMSStandardModule["Tangent and residual"] in AceGen and want to use command ToSphericalCoordinates for but AceGen is ...
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### How to simplify complex Trigonometric expression in mathematica? [closed]

The expression which I need to simplify in mathematica into simplest form ...
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### Does Mathematica know about trig identities?

I am calculating some geometry via two different ways in Mathematica. One uses a known trig identity the other doesn't. We define angles of two right-angle triangles. ...
67 views

### Removing transient part in equation and solving for a general form

I have the following code that I run: ...
102 views

### NIntegrate fails to solve a double oscillatory integral

I need to compute the following integral: ...
63 views

### How solve this system of trigonometric equations?

I have the following system of equations: (substituting any real values for a,b,c,r,Alpha,Beta will return the same answer for x) ...
146 views

### Returning trigonometric value answers in irrational form

I need to find the irrational form of Sin[7*\[Pi]/8]. But in Mathematica, I can get its numerical value. I am getting ...
1 vote
64 views

### Why if I change the function Sine to discrete Sine the plot is difference

I would like to know why when I change +1 in a discrete Sine change the list line plot and when I plot the function sine anything change. ...
1 vote