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+ ...
166 views

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: <...
72 views

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?
43 views

Cannot seem to find the syntax to evaluate a trig expression [closed]

3*Cos[t] == Cos[Sqrt[3]*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 ...
39 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 ...
135 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: ...
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 \...