# Questions tagged [trigonometry]

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

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### Does Mathematica know about identity involving ArcSin(Cos(x))? [duplicate]

Given that $0 < x < \pi/2$, it can be shown that $$\arcsin(\cos(x)) = \pi/2-x,$$ however, I was unable to make Mathematica to simplify the LHS into the RHS. I was guessing that, ...
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### Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
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### Trigonometric identity not simplifying

I have a pair of numbers {x,y} (Reals or Integers) for which I want to confirm symbolically that ArcTan[y/x]+ArcTan[x/y]==Pi/2 Here is my attempt: ...
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### Elimination of trigonometric functions [closed]

I want to eliminate $\gamma$ from the system of equations given below: ...
168 views

### Finding points in a plane

The end of the Star Wars saga is near, so I feel compelled to design a Mouse Droid. Based upon the Paul Murphy's schematics I've reconstructed the outline of the top shell: Since my goal is to ...
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### How can I solve this trigonometric equation system?

As the picture shows,there are four equations and three angles,\theta1,\theta2,\theta3. I need to solve the values of this three angles. If the range of the angles needed, then consider (-Pi,Pi). BTW, ...
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### Minimal Surface of Revolution - Integrate Challenge

I'm trying to use Mathematica to go from equation (11) to equation (12) in this example of a Minimal Surface of Revolution. There is a MMA notebook on that link, but it only shows how to find the ...
58 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 ...
44 views

### 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 ...
297 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 ...
276 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 ...
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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: ...
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### 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 ...
98 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%...
41 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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### 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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### 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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### 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 ...
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### 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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### Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
309 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 ...
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### 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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### How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...