# 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 ...
• 145k
1 vote
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, ...
• 195
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 ...
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### Solution for equation in degrees

I have a equation to which i would like to find out all the possible solutions ...
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: ...
• 1,699
1 vote
81 views

### Simplification of trigonometric expressions

I would like to automate the simplification of certain trigonometric expressions, such as ...
1 vote
54 views

### My sinusoidal fit requires an unused extra constant to work

I am trying to fit a sinusoidal curve onto the following data: ...
1 vote
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] ...
• 4,315
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 ...
• 1
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, ...
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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 ...
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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 ...
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 ...
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### 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 ...
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 ...
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### 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 ...
• 4,315
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? ...
• 4,315
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 (...
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 ...
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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 +...
• 3,677
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 ...
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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 ...
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 ...
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1 vote
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 ...
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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] <...
• 4,315
1 vote
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 <...
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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 ...
• 4,315
1 vote
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 ...
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1 vote
93 views

### Solve equation - Error - Help

I need to find the value of n but I get an error. I used this: ...
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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 ...
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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 ...
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1 vote
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 $\cos(2\theta)$ ...
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159 views

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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]==?
• 4,315
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 ...
• 145k
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 ...
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 ...
• 361
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 ...
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1 vote
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(\...
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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, ...
1 vote
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. ...
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258 views

### Collect the coefficients through the Cos argument

I have for example the following expression: ...
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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 (...
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1 vote
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}\...
• 2,141
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 ...
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 ...
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 - ...
• 1,293
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: ...
1 vote
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 ...
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