# Questions tagged [trigonometry]

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

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### Solving multivariable trig Identities

I'm trying to solve for a certain set of trig identities in terms of other trig identities. I saw this and this, but in my example, I have two tries: ...
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### Reduce yields ArcTan instead of Pi/4

I expect this call: Reduce[Sin[x] - Cos[x] == 0, x, Reals] to return $x = \pi/4 + 2k\pi \ \vee \ x = -3/4 \ \pi + 2k\pi$. However, $\pi/4$ and $3/4\ \pi$ get ...
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### How to get the result of TrigFactor in terms of Cos

If I use TrigFactor, it gives the result in terms of Sin: In[483]:= expr := Cos[x] + Sin[x] TrigFactor[expr] Out[485]=Sqrt[2]*Sin[Pi/4 + x] What I want to get is <...
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### Why can I not numerically integrate a smooth, integrable function?

Consider the function $\csc(t)\sin(3t)$ on the interval $[0,\pi]$. This is a perfectly well-behaved smooth function, as can be seen when plotting it: ...
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### Any way to get Mathematica to Solve[Sin[Tan[x]]-Tan[Sin[x]]==0,x]?

Solve[Sin[Tan[x]] - Tan[Sin[x]] == 0, x] It says it runs out of methods. After a very long time. Plotting the expression shows there are periodic solutions and ...
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### Why reduce does not give solution for ArcTan[Tan[x]] == x?

Basic question I can't see why now. This works Simplify[ArcTan[Tan[x]] == x, Assumptions -> -Pi/2 < x < Pi/2] (*True*) But ...
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### Why doesn't Mathematica know the exact value of some trivial trigonometric functions?

The trigonometric functions for half angles have well-defined and simple rules. For example $$\tan\left(\frac x2\right)=\frac{\sin x}{1+\cos x}=\frac1{\csc x+\cot x}$$ But I can't get the exact value ...
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### How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
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Find the value range of real number a, so that for any real number x and $\theta \in\left[0, \frac{\pi}{2}\right]$, make \$(x+3+2 \sin \theta \cos \theta)^{2}+(x+a \sin \theta+a \cos \theta)^{2} \...