Questions tagged [trigonometry]
Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.
495
questions
4
votes
1
answer
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How to force Mathematica to simplify in terms of half angles?
By basic trigonometric identities, the expression $\frac{\sinh(x)}{\sqrt{2}\sqrt{1+\cosh(x)}}$ simplifies to $\sinh(\frac{x}{2})$. But Mathematica seemingly don't perform this simplification. I tried ...
- 43
3
votes
0
answers
75
views
Mathematica's definition of cos(kA) where A is the 1st Pauli spin matrix [closed]
For a homework assignment I was asked to derive the formula of $e^{ik\sigma_{1}}$ - where $\sigma_{1}$ is the Pauli spin matrix {{0,1},{1,0}} - using the Taylor ...
0
votes
0
answers
46
views
how to get the set of coefficient of a trig function in terms of the sines and cosines of a given angle
Say I have an expression like this
a Sin[\[Theta]]^4 + b Cos[\[Theta]]^4 +
c Sin[\[Theta]]^3 Cos[\[Theta]] + d Sin[\[Theta]]^2 + e=0
My ultimate goal is to solve ...
- 695
3
votes
3
answers
249
views
Drawing angle bisectors in a triangle
In triangle $\triangle ABC$, the angle $\angle BAC$ is equal to $60°$, $|AB|=2$, $|BC|=\sqrt 6$, and $AD$ bisects the angle $\angle BAC$ and $BC$ at point $D$.
How can I find the length of the angle ...
- 2,879
-2
votes
2
answers
96
views
Reduce and Solve give incorrect answers for trigonometric equation [closed]
Why use Reduce and Solve to solve the Trigonometric functions equation with incorrect results?
...
- 2,879
0
votes
1
answer
73
views
Find the interval that satisfy the equations
I am having issues solving rather simple equations with these functions.
The equations are
I have plotted each equation and its obvious that there are multiple solutions to these equations (...
6
votes
3
answers
152
views
Simplify solutions of trigonometric equation has the form Sin[a]==Sin[b]
I am trying to solve the equation
$$ \sin\left(2 x + \dfrac{\pi}{5} \right) = \sin \left(3 x-\dfrac{2 \pi }{7} \right). $$
My code
...
- 2,585
5
votes
0
answers
111
views
Simplify solution of trigonometric equation
I use this code to solve equation Sin[2x]==0]
Reduce[Sin[2 x] == 0, x]
C[1] ∈
Integers && (x == π C[1] || x == 1/2 (π +...
- 2,585
0
votes
1
answer
97
views
How can I draw a triangle and find the length of its height?
Given that the sum of three inner angles $a,b$ and $c$ in a triangle is $\pi$, and knowing that：
$$2 \sin(a−c) = \sin b,$$
$$a+b=3c,$$
how can I draw this triangle and find the length of the height on ...
- 2,879
0
votes
0
answers
38
views
Invalid Variable Error for Solve When Using Law of Cosines
I'm making a shadow simulator, and am using the Law of Cosines to calculate a certain angle in a triangle with two known widths and one known angle. I'm using Solve ...
0
votes
1
answer
68
views
3D plot not working, find max/min points [closed]
Im trying to plot this graph in mathematica:
(x+y)sin(x-y)
And this is my in- and output:
Plot3D[(x + y) (Sin[x - y]), {x, -50, 50}, {y, -50, 50}]
The output is ...
- 27
1
vote
3
answers
143
views
How to find the maximum value of a parameter [Omega] in a trigonometric function?
The form of the known trigonometric function is:
f[x_] := Sin[ω x + ϕ]
The known conditions are:
ω > 0, ϕ ∈ {0, 2 π}
One of ...
- 2,879
3
votes
5
answers
460
views
How to find the maximum value of this trigonometric function?
The known conditions are:
Sin[2 α + β] ==
2 Sin[β], 0 < α < π/2, 0 < β < π/2
Find the maximum value of Tan [β]
<...
- 2,879
1
vote
3
answers
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views
How to solve this trigonometric function equation?
Solve[{TrigExpand[Tan[2 α]] == Cos[α]/(2 - Sin[α]),
tanα == Sin[α]/Cos[α],
0 < α < π/2}, tanα, {Sin[\[Alpha]], Cos[\[Alpha]]}]
It returns <...
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3
votes
2
answers
176
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How can expanding trigonometric function retain an expression?
I want to expand this trigonometric function
Sin[π/4 + α - β]
such that $\alpha - \beta$ is treated as "one" expression, resulting in
...
- 2,879
1
vote
1
answer
78
views
Solving a trigonometric equation for the angle in radian
I have been trying to solve the following equation in radians:
NSolve[0.6` Cos[π/6 + 2.` x ] + Sin[x] == 0, x]
Following this, I can modify the code as
...
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1
vote
1
answer
79
views
0
votes
1
answer
70
views
How to switch Tan[x] for Sin[x]/Cos[x] without Mathematica changing the latter for the former? [duplicate]
When I ask Mathematica to do this:
(Sin[2 x] - Tan[2 x])/x^3 /. Tan[x_] -> Sin[x]/Cos[x]
It makes no change because Mathematica interprets ...
- 5,121
2
votes
3
answers
145
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Evaluate using Mathematica or otherwise $\int_{0}^{\pi/2}\sin^n x \ T_n(\sin x)\ dx$
Denote $T_n(x)$ as Chebyshev polynomial of the first kind (see here). Then I need to evaluate for $n$ a odd natural number $$\int_{0}^{\pi/2}\sin^n x \ T_n(\sin x)\ dx $$
I am requesting a code with ...
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1
vote
0
answers
45
views
Expression of trigonometric function
I have a complicate expression with a lot of trigonometric functions. And I want to express the function just in the form of $\cos(\theta)$ and $\sin(\theta)$ instead of something like $\cos(2\theta)$ ...
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0
votes
2
answers
89
views
0
votes
1
answer
102
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Given the trigonometric value of the double angle, how to find the trigonometric value taught by double？
Known this
Tan[2 A] == 2 Sqrt[2]
How do you evaluate its value?
Tan[A] ==? Sin[A]==? Cos[A]==?
- 2,879
3
votes
2
answers
136
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Is there an option to automatically make solve return the principal value of inverse trig functions?
I am porting some of my Maple packages to Mathematica. In Maple, solve(sin(y)=x,y) returns arcsin(x) and I'd like to get same ...
- 137k
5
votes
4
answers
629
views
How to calculate the integral only in real domain?
I have the following integral:
Integrate[1/(Sqrt[2] + Cos[4 X] + Sin[4 X]), X,
Assumptions -> Element[X, Reals]] // Simplify
...
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2
votes
1
answer
103
views
How can I make sure that the two given numbers are exactly the same?
I have the given numbers $n1$ and $n2$. How can I make sure that these two numbers are exactly the same? Numerically, using {N[n1,40], N[n2,40]}, by increasing the ...
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0
votes
2
answers
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Solving a polynomial in trigonometric functions
Given all variables are in $\mathbb{R}$, and $\{ a, d\} \neq 0$, solve for $\theta$:
$$a \sin^2 \theta + b \sin \theta + c + d \cos^2 \theta + e \cos \theta + f = 0$$
as posed in this question.
The ...
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1
vote
2
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83
views
How to ask Mathematica to rewrite the larger arguments of sine function as a smaller number which is multiple of $\frac{2\pi a}{11}$
I have a trigonometric function $Exp$ where $\{f,g,h,k\}$ are some parametric functions, and $a\in\mathbb{N}$ and $x>0$.
$$ Exp=f \cdot \sin \left(\frac{58 \pi a}{11}+x\right)+g\cdot \sin \left(\...
- 1,159
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0
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How does this trigonometric simplifier work?
I recently watched this video of Wolfram channel about modelling black holes with Mathematica. https://www.youtube.com/watch?v=bOtvvw1dyN0 At 13:45
In it, they have created a trigonometric simplifier, ...
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1
vote
0
answers
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Simplification problem using trigs
given
f1 = Sin[x]/Sqrt[2 + Sin[2 x]]
f2 = (Cos[x]-Cos[3 x]+4 Sin[x])/(2 (2+Sin[2 x])^(3/2))
These are same for all x.
...
- 137k
5
votes
3
answers
220
views
Collect the coefficients through the Cos argument
I have for example the following expression:
...
- 137
2
votes
1
answer
94
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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 (...
- 21
1
vote
0
answers
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views
Power of trigonometric function matrix [closed]
Calculate the m-power of the following trigonometric function matrix (m>0):
$\boldsymbol{A}=\left(\begin{array}{cc}\cos \varphi & -\sin \varphi \\ \sin \varphi & \cos \varphi\end{array}\...
- 1,943
4
votes
1
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How can I have Mathematica solve the curve equation when nested functions are involved?
In the context of Quantum Computing, I am investigating curves that illustrate an error propagation during qubit rotations on a Blochsphere (I asked a related question in the same context here and ...
- 315
3
votes
0
answers
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Cannot Understand nth Derivative of x/ArcTan[x]
The nth derivative of x/ArcTan[x]:
f[x_, n_] = D[x/ArcTan[x], {x, n}]
Evaluates to:
I cannot get this general from to return ...
3
votes
2
answers
131
views
Replacing a trigonometric value
It looks like MMA cannot evaluate Tan[42°] but it can be written as
(-Sqrt[6 - 2 Sqrt[5]] + Sqrt[6 (5 + Sqrt[5])])/(2 Sqrt[7 - ...
- 1,273
0
votes
1
answer
85
views
Unable to simplify exponential expression to its simplest form of trigonometric expression by Euler's formula
Applying "FullSimplify" fails to simplify the following expressions:
Input:
...
- 3
1
vote
1
answer
156
views
convert n*Arctan[x] to ArcTan[x]
In the result of solving the equation or the integral often get something like k*ArcTan[x], I prefer the ArcTan[x] form.
For ...
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4
votes
3
answers
292
views
How to build an inscribed circle in a triangle on a sphere?
I want to build an inscribed circle into a triangle on a sphere. To do this, I first build its center - the intersection point of the bisectors. But there were problems with finding it. I build the ...
- 41
1
vote
1
answer
171
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Solving multivariable trig Identities
I'm trying to solve for a certain set of trig identities in terms of other trig identities. I saw this and this, but in my example, I have two tries:
...
- 11
2
votes
1
answer
81
views
Reduce yields ArcTan instead of Pi/4
I expect this call:
Reduce[Sin[x] - Cos[x] == 0, x, Reals]
to return
$x = \pi/4 + 2k\pi \ \vee \ x = -3/4 \ \pi + 2k\pi$.
However, $\pi/4$ and $3/4\ \pi$ get ...
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7
votes
2
answers
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How to pose simultaneous trigonometric equations problem in a way solvable by mathematica
Context:
A camera at O has an image of a rectangular object ABCD.
From the 2D coordinates of the image + the projection matrix of the camera I can calculate the direction vectors $\hat {A}, \hat{B}, \...
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0
votes
0
answers
107
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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 ...
- 135
2
votes
1
answer
84
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.
<...
- 659
9
votes
6
answers
608
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 ...
- 553
4
votes
2
answers
178
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 ...
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4
votes
1
answer
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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 <...
user49048
1
vote
0
answers
37
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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 ...
- 111
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votes
5
answers
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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 ...
- 1,648
2
votes
1
answer
95
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 ...
- 2,364
1
vote
1
answer
154
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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