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Questions tagged [trigonometry]

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

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How to obtain this solution for first order ode using DSolve? ArcSin issue with IC

This is tricky problem from textbook. Mathematica DSolve can't solve it. Maple gives same solution as given in back of textbook. First will show the problem ...
Nasser's user avatar
  • 145k
1 vote
0 answers
71 views

How can I ask Mathematica to give the explicit real form of the given function?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
MsMath's user avatar
  • 195
0 votes
1 answer
60 views

Tan function problem [closed]

Why does the Tan function give values for 0, and 30 Degree, but not for the others? Strange behavior? In[16]:= Tan[0 Degree] Out[16]= 0 In[23]:= Tan[10 Degree] Out[23]= Tan[10 °] In[24]:= Tan[20 ...
user3584513's user avatar
0 votes
1 answer
66 views

Solution for equation in degrees

I have a equation to which i would like to find out all the possible solutions ...
Anshul Bokade's user avatar
0 votes
1 answer
105 views

ExpToTrig conversion problem

Let we have some ODE solution: formExp = c1 E^(-I t) + c2 E^(I t) +c3 E^(-2 I t) + c4 E^(2 I t) It is known that this solution can be reduced to the form: ...
lesobrod's user avatar
  • 1,699
1 vote
1 answer
81 views

Simplification of trigonometric expressions

I would like to automate the simplification of certain trigonometric expressions, such as ...
Sheparcapea's user avatar
1 vote
0 answers
54 views

My sinusoidal fit requires an unused extra constant to work

I am trying to fit a sinusoidal curve onto the following data: ...
Zeke Coady's user avatar
1 vote
1 answer
98 views

Converting trigonometric expressions between sine and cosine forms

How to convert sine and cosine into each other? Using the relationship between sine and cosine for mutual transformation: Such as: Sqrt[3] Sin[π/6 - (π x)/4] ...
csn899's user avatar
  • 4,315
0 votes
1 answer
112 views

Solving a system of 8 nonlinear equations

I'm new on Mathematica and have been trying to solve the following system of 8 equations with 7 variable: However, Mathematica takes too much time trying to solve the system. I left Mathematica ...
EeeE's user avatar
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0 votes
1 answer
72 views

How can I improve this weird FullSimplify result?

I can't seem to get FullSimplify to fully simplify this complicated expression. I've added relevant Assumptions that helped, ...
Jerry Guern's user avatar
  • 4,612
5 votes
1 answer
120 views

Why do Resolve and ForAll fail with trigonometric expressions?

Why Resolve is not able to solve this problem? Similarly Solve and Reduce are not able to do ...
azerbajdzan's user avatar
  • 18.8k
6 votes
3 answers
527 views

Sum of sinusoids at the same frequency but with different amplitudes and phases

Three sinusoids at the same frequency are superimposed: Cos[3.1 - t] + 5 Cos[π/4 + t] + 2 Sin[0.3 + t] How can the resulting oscillation be stated in the following ...
saturnscalypso's user avatar
5 votes
1 answer
138 views

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 ...
Sanjana's user avatar
  • 173
3 votes
0 answers
83 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 ...
Raketenmensch 's user avatar
0 votes
0 answers
48 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 ...
larry's user avatar
  • 735
3 votes
3 answers
270 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 ...
csn899's user avatar
  • 4,315
-2 votes
2 answers
106 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? ...
csn899's user avatar
  • 4,315
0 votes
1 answer
76 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 (...
Ihab Alrikabi's user avatar
6 votes
3 answers
156 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 ...
minhthien_2016's user avatar
5 votes
0 answers
113 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 +...
minhthien_2016's user avatar
0 votes
1 answer
115 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 ...
csn899's user avatar
  • 4,315
0 votes
0 answers
41 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 ...
LonelySpaceman's user avatar
0 votes
1 answer
74 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 ...
Kei Len's user avatar
  • 27
1 vote
3 answers
153 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 ...
csn899's user avatar
  • 4,315
3 votes
5 answers
477 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] <...
csn899's user avatar
  • 4,315
1 vote
3 answers
196 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 <...
csn899's user avatar
  • 4,315
3 votes
2 answers
187 views

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 ...
csn899's user avatar
  • 4,315
1 vote
1 answer
102 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 ...
PoreyS's user avatar
  • 635
1 vote
1 answer
93 views

Solve equation - Error - Help

I need to find the value of n but I get an error. I used this: ...
Zarabu's user avatar
  • 81
0 votes
1 answer
86 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 ...
Red Banana's user avatar
  • 5,391
2 votes
3 answers
153 views

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 ...
Max's user avatar
  • 145
1 vote
0 answers
62 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 $\cos(2\theta)$ ...
Gabriel's user avatar
  • 73
-1 votes
3 answers
159 views

How to find the relationship between angle an and angle b from the equality relation?

...
csn899's user avatar
  • 4,315
0 votes
1 answer
114 views

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]==?
csn899's user avatar
  • 4,315
3 votes
2 answers
188 views

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 ...
Nasser's user avatar
  • 145k
5 votes
4 answers
662 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 ...
Anna Schmidt's user avatar
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 ...
Phys96's user avatar
  • 361
0 votes
2 answers
196 views

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 ...
David G. Stork's user avatar
1 vote
2 answers
98 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(\...
charmin's user avatar
  • 1,159
0 votes
0 answers
76 views

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, ...
Johnset's user avatar
1 vote
0 answers
62 views

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. ...
Nasser's user avatar
  • 145k
5 votes
3 answers
258 views

Collect the coefficients through the Cos argument

I have for example the following expression: ...
Luis Renato's user avatar
2 votes
1 answer
108 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 (...
Ji'an Li's user avatar
1 vote
0 answers
47 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}\...
lotus2019's user avatar
  • 2,141
4 votes
1 answer
86 views

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 ...
Eldar Sultanow's user avatar
3 votes
0 answers
132 views

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 ...
Josey Stevens's user avatar
3 votes
2 answers
133 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 - ...
mf67's user avatar
  • 1,293
0 votes
1 answer
96 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: ...
Jeremy's user avatar
  • 3
1 vote
1 answer
165 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 ...
expression's user avatar
  • 5,652
4 votes
3 answers
340 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 ...
Michael's user avatar
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