Questions tagged [trigonometry]

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

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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 ...
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Solving complex trig quations - missing solutions?

{ Sin[Pi/2 + I*Log[2 + Sqrt]], Sin[Pi/2 - I*Log[2 + Sqrt]], Sin[Pi/2 + I*Log[2 - Sqrt]], Sin[Pi/2 - I*Log[2 - Sqrt]] } // FullSimplify ...
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Solar Power Calculations

Good Afternoon, I have calculated the Incident beam radiation for a given locations local sunlight hours. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: ...
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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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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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 ...
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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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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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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 ...
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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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Finding the functions that Mathematica plots while using BodePlot

I've the following Mathematica-code: ...
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 ...
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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 ...