Questions tagged [trigonometry]

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

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1answer
45 views

Simplify product of cosh and sech expressions

I would like to simplify a product of hyperbolic cosine and hyperbolic secant functions, with the key simplifying assumption being that the two are inverses of each other. This sounds like a silly ...
2
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1answer
41 views

Solving complex trig quations - missing solutions?

{ Sin[Pi/2 + I*Log[2 + Sqrt[3]]], Sin[Pi/2 - I*Log[2 + Sqrt[3]]], Sin[Pi/2 + I*Log[2 - Sqrt[3]]], Sin[Pi/2 - I*Log[2 - Sqrt[3]]] } // FullSimplify ...
3
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2answers
83 views

Solar Power Calculations

Good Afternoon, I have calculated the Incident beam radiation for a given locations local sunlight hours. ...
0
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1answer
67 views

how to solve equations

I am trying to find the values of L and \theta, but mathematica is unable to produce output. My code is given below, where the value of k is fixed, i.e., 0.75, but the value of B can be positive or ...
9
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1answer
286 views

Why ArcTan[1, 0. I ] yields -1.5708+0. I?

Bug introduced in 5.2 or earlier and persisting through 12.0.0 Why ArcTan[1, 0. I ] yields -1.5708+0. I ? The result should ...
2
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4answers
251 views

How to derive trigonometric Cartesian equation from parametric

How can one derive programmatically a Cartesian equation when $x$ and $y$ are parametrically represented by trigonometric functions? i.e.: Given that $x= \cos(2 t)$, and $y = -\sin(t)$, how can I ...
0
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2answers
43 views

FullSimplify not finding trig substitution with other terms present

Consider the following: FullSimplify[Cos[x - y - z] + Cos[x + y + z] + 1] Mathematica simply returns the exact expression with no simplification. However, if I ...
2
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1answer
35 views

Finding the 3D-model of a function that is rotated around the x-axis

How can I find the 3D model that is created by revolving the function: ...
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0answers
47 views

Convert Part of an Expression Using ExpToTrig

I'm wondering if there's a nice way to convert only parts of an expression, say exponential functions of varible $\theta$ to trig. The motivation is best descripbed by the following example. ...
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0answers
39 views

How to solve this trigonometric equation

The equation Sin[9 x - Pi/3] == Sin[7 x - Pi/3] can solved by hand Reduce[9 x - Pi/3 == 7 x - Pi/3 + k 2 Pi, x] x == ...
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2answers
77 views

How can I get solutions of this trigonometric equation?

I am trying to solve the equation $$\left(\sin (x)+\cos (x)-\sqrt{2}\right)\cdot \sqrt{-11 x-x^2-30}=0$$ in Real domain. I tried First way ...
2
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1answer
79 views

Combining ArcTan's like in Maple

It seems to me there is no simple way to combine ArcTan's with complex arguments symbolically in Mathematica as it is in Maple (https://www.maplesoft.com/support/help/Maple/view.aspx?path=combine%...
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40 views

Trigonometric derivation using Solve

Background: I'm trying to derive the relation between two variables in an optical system. The derivation is simple and well-known in the limiting case ($H \to \infty$, see figure), but rather tricky ...
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2answers
39 views

NSolve cannot find solution to system of trig equations

I was making a program to convert a rotation matrix to a set of euler angles. I wanted to do this for any valid rotation order that the euler angles were made with, and I did not want to do it the ...
0
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1answer
45 views

Complex Exponentials to Trig Functions?

I have an expression expr = 1/2 a E^(-3 I ω t) (E^(3 I ω t)+2 Cos[π x/a]) (1+2 E^(3 I ω t) Cos[π x/a]) Sin[π x/a]^2; expr // TeXForm $\frac{1}{2} a e^{-3 i t \...
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0answers
43 views

Different integration results when TrigToExp used

I am trying to do a double integral over a domain $x \in (\theta_1,\theta_2), y \in (0,\theta_1)$. Instead of doing a definite integral I am doing an indefinite integral and taking limits. All that is ...
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2answers
92 views

How can I add two sin waves of different amplitude and frequency? [closed]

I've been tearing up the internet, but I can only find explanations for adding two sine waves of same amplitude and frequency, two sine waves of different amplitudes, or two sine waves of different ...
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0answers
38 views

Survey Question

Question for Civil Engineer or Surveyor I have a hypothetical question relative to the earth (sphere) and a square piece of land. If I buy a piece of land at the equator that is 1000 miles by 1000 ...
2
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2answers
127 views

FullSimplify a trigonometric expression doesn't work as expected

I know this kind of question is frequent asked, yet each case has its own particularities. I will show my problem. I define the following: ...
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1answer
35 views

Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) i.e $$ \frac{1}{2} (-2 \pi \...
4
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1answer
83 views

How to convert Sine to Cosine?

I have some trigonometric quantities, which may be expressed in either sine or cosine, e.g., ia = Cos[wt], ib = -Sin[π/6 + wt], <...
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0answers
52 views

How to automatically transform Abs[Cos[x]]Sec[x] to Sign[Cos[x]]?

Out of some simplification, the term Abs[Cos[x]]Sec[x] appears. How can I make the code automatically transform ...
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1answer
56 views

Using constraints when solving a trigometric equation [closed]

I'm trying to learn how to add constraints/assumptions to equations when using Solve, sp as to avoid multi-valued solutions. For example, I'm trying to use ...
3
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0answers
36 views

Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify] Are not correctly evaluated to: True? What is the ...
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1answer
27 views

Variable value is changing inexplicably [closed]

So I was trying to avoid doing some trig calculations on paper by using mathematica, when I encountered this (Screenshot in a new notebook, after having restarted everything): As you can see, B is ...
2
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1answer
77 views

Prevent simplification of trig functions

Mathematica often simplifies trigonometric expressions, for example replacing $\sin(\frac{\pi}{4})$ with $\frac{1}{\sqrt{2}}$, or replacing $\cos(\frac{3\pi}{8})$ with $\sin(\frac{\pi}{8})$. I'd like ...
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5answers
1k views

Fitting a Cos^2 function

I have to fit a Cos^2 function to data I measured. The function is $a \cos^2(\frac{bx\pi}{180}+c)+d $ and I tried the FindFit and Linear Model Function. I have 4 datasets which I have to fit, the ...
5
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4answers
173 views

Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
4
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2answers
669 views

Mathematica gives an unexpected answer for Integrate [closed]

I need to integrate the following: \begin{equation}\tag{1} \frac{\sqrt{C + (1 - C) x^3}}{x}, \end{equation} where $0 < C < 1$ and $x$ is a positive variable (then $x^3 \ge 0$). When I integrate:...
6
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1answer
85 views

Computing the seven roots of a polynomial

This question was originally asked by @fsrong70 six months ago. The OP deleted it shortly after posting and has not returned to this site since. I had just figured it out when it was deleted. I ...
3
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1answer
67 views

Simplifying symbolic integration with trigonometric functions

I am using DSolve to verify a multitude of definite integrals I have done by hand, and things have gone perfectly until this integral, $$ \int_0^t \frac{\mathrm{d}...
3
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4answers
288 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
11
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3answers
294 views

Simplifying Cosh[a] + Sin[a] + Sinh[a]

Why does FullSimplify[Cosh[a] + Sinh[a] + Sin[a]] not return Exp[a]+Sin[a] ? Is this some bug in Mathematica or am I being ...
0
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1answer
62 views

Different solution on trigonometric function in mathematica and wolframalpha using Simplify and FullSimplify [closed]

I have this expresion: -cos(a3) (cos(a2) sin(a1) + cos(a1) sin(a2)) And when I simplify with wolframalpha online, it give me this: ...
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1answer
138 views

How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...
0
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1answer
114 views

Blood Pressure problem given equation [closed]

The blood pressure (P) of an individual after t seconds with a heart rate of 70 beats/min. can be modeled by the function, P(t) = 100 + 20 sin(7π/3)t In the time interval from 0s ...
0
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1answer
251 views

Trouble plotting P(t) = 100 + 20 sin(7π t/3) [closed]

I'm trying to plot this but I keep getting an empty graph. I put in: Plot[P[t_] := 100 + 20 sin[(7 pi)/3] t, {t, 0, 10}]
0
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1answer
167 views

I need to solve this equation: 2 cos^2 θ − 7 cos θ − 4 = 0 on the interval 0 ≤ θ < 2 π [closed]

I've been trying to solve the problem, but I keep getting errors.Thanks for the help.
1
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1answer
48 views

Solve command doesn't work (i'm beginner)

I try to perform the equation by writing: ...
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1answer
68 views

Interpretation of PolarPlot

I tried to plot the function $r=-2t$ with $t$ in $[0,2\pi]$: PolarPlot[-2 t, {t, 0, 2 Pi}, AxesLabel -> {x, y}] When $t=\pi/4$, I have: $$r=-\pi/2=-1.57$$ ...
0
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1answer
72 views

FullSimplify not simplifying expression containing the form Sin[n] where n is an integer [closed]

I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why? ...
3
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1answer
61 views

Generating trigonometric sums

How can one generate all cosine polynomials with $\pm1$ coefficient of following form: $$\sum_{k=1}^n\pm\cos kt.$$ I tried DO loop but couldn't get all of them as clearly cannot exhaust $2^n$ ...
2
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1answer
123 views

Domain and codomain of a function

I am wondering if it is possible to get domain and codomain of a function in Mathematica (by using only built-in functions if possible). For example, I would like to give as input the function $tan(x)$...
4
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4answers
306 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
3
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1answer
75 views

Given two lines find the four circles that have the lines as tangents

Given two lines, each defined by two points, and a radius find the four circles that have the lines as tangents. I give my attempt below but there ought to be a nice mathematica way of doing this. <...
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0answers
43 views

Finding the functions that Mathematica plots while using BodePlot

I've the following Mathematica-code: ...
2
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2answers
159 views

Fourier Phase Angle Interpretation

I am trying to fit the following tide data (taken from here) with a sinusoidal curve that looks like the following: displacement+amplitude * sin(t w - ph), where t is the independent variable, w is ...
1
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1answer
53 views

Plot contour of zeroes against trig function

Take two functions: func1=Cos[Pi*x]*Cos[Pi*y] func2=x Sin[Pi*x] I want to create a plot that shows a 2D contour map of ...
1
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1answer
44 views

Strange output for solve in terms of trigonometric functions

I am using the following Solve code: ...
0
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1answer
71 views

Defined function doesn't plot correctly

I have defined a function that produces a single negative impulse spanning -b to -a and a positive impulse spanning ...