# Questions tagged [trigonometry]

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

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### Solving a system of trigonometric equations. with NSolve

Is numerical solving of the problem in the picture below even possible? Edit: The code does not output anything, it just runs for 20min+ ...
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### Solve can't solve my trigonometric equation—why?

I have the following equation for epsilon $2 |\alpha_{n,ch}|=\epsilon+\cos^{-1}(\tan(\frac{\pi}{4}-\frac{\epsilon}{2}))$, where $\alpha_{n,ch}$ is a negative constant (e.g. -0.769) I tried to solve ...
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### Evaluate the defining Integral of the Bessel functions of the first kind

I am trying to evaluate the integrals $$\int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}(x\sin t - nt)} \mathrm{d}t$$ and $$\int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t$$ ...
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### How do I apply complicated algebraic/trigonometric manipulations to nested expressions?

Consider the expression $$a\sin(x)-a\sin\left(\frac{x}{a}\left(a+\frac{ay}{x}\right)\right) \label{a}\tag{1}$$ which can be rewritten as $$\sin(x)-\sin\left(x+y\right) \label{b} \tag{2}$$ and ...
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### How to get Trig Form from Root

Simplify`TrigToRoot[Cos[Pi/9]] gives out Root[-1 - 6 #1 + 8 #1^3 &, 3] But when I want to do the inverse operation: <...
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### Atan2 function unwrap [closed]

I use atan2 function in my calculations. The results are as follows: Matlab has the unwrap function, and it copes well with the correction of such plots. How to do it in Mathematica?
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### Cannot seem to find the syntax to evaluate a trig expression [closed]

3*Cos[t] == Cos[Sqrt*t] between the values t=0 and t=1 Thanks for any help.
116 views

### Volume integration with a condition

I have a set of parameters $x_1, \dots x_4 \in (0,1)$. I want to find the volume of the subregion of this 4d cube satisfying $$\sin^{-1}(x_1)+ \dots +\sin^{-1}(x_4) > \frac{3\pi}{2}$$ I've tried ...
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### 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 ...
116 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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### 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: ...
338 views

### How can Mathematica simplify this trigonometric function?

This question must be too simple, but it confused me for several days. I want to know how can I do the following simplification using Mathematica: For example, convert ...
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 \...