# Tagged Questions

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

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### Use the trigonometric identities to expand and simplify if possible [on hold]

Use the trigonometric identities to expand and simplify if possible. A, cos(270∘−θ) B, sin(270∘−θ) C, cos(270∘+θ) Here is my answers, it needs checking. 1. cos(270 - theta) = cos( 180 +90 - ...
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### Simplify trigonometric equation knowing that $sin(a)=n*sin(b)$

I was working on a problem involving trigonometry. I used Mathematica to help me in solving it. I ended up with this formula: ...
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### Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?

Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, ...
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### TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...
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### Solving/simplifying a trig function [migrated]

Given: $\tan\:a=\frac{5}{12}$ and $a\in QIII$ $\csc\:B=-\frac{5}{4},\:\cos\:B>0$ $\cos\:\theta =-\frac{8}{17},\:\frac{\pi }{2}<\theta <\pi$ Solve: ...
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### Solving/simplifying a trig expression [migrated]

My problem sheet says that $\tan a= 5/12$ and $a \in {\rm Q\,III}$ ($a$'s in quadrant III). Using this information, I am to solve/simplify the expression $\quad \quad \cos\left(\frac{1}{2}a\right)$ ...
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### Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)

I'm trying to simplify an expression with sums of ArcTan, for which I've written a transformation rule that works for simple sums, so that ...
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### Simplification of (Co)sine of a sum

I have a huge expression with (Co)Sine of a sum like Cos[[Theta] - 2 [Phi]] (after using \Simplify). I wanted to know if it exists a function which forces Mathematica to express the result in terms of ...
63 views

### strange result with trigonometric triple integral [duplicate]

I'm defining functions e[k_, t_] := Cos[Pi (k - 1) t] cosIntRaw[k_, l_, m_] := Integrate[e[k, t] e[l, t] e[m, t], {t, 0, 1}] cosInt[k_, l_, m_] := Assuming[Element[{k, l, m}, ...
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### how can tangent half angle substitution be done in Mathematica?

Is it possible to replace sine and cosine in terms of tangent half-angles and again the tangent half-angles by a variable say t?
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### Is it possible to simplify a trigonometric expression only in terms of $\cos (u)$ OR $\sin (u)$?

I want to expand the following expression into powers of $\cos(u)$ only: a1 + a2 Cos[2 u] + a3 Cos[4 u] + a4 Cos[6 u] The answer that I want (and which I found ...
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### Prevent trigonometric simplification [duplicate]

I have created a plot of g(x)=a*sin(b(x-c))+b where a, b, c, and d change using sliders excetera. Also, the trig function itself func = (sin, cos, tan) is selected using buttons. My issue is with the ...
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### DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
566 views

### Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
141 views

### Mathematica not recognising closed forms as specific values

I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using ...
233 views

### Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
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I have ...
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### Fitting data using a series of Sin and Cos

I have the following data representing the normal displacement caused by a normal load applied at the middle cross section of a cylinder: I've made the data available here. I am trying to fit ...
438 views

### Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
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### Prevent FullSimplify from converting trigonometric expressions to exponential

There's an option for FullSimplify, which is Trig, and with it I could prevent a trigonometric identities from being used. I'm ...
81 views