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Questions tagged [trigonometry]

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

5
votes
4answers
143 views

Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
0
votes
0answers
11 views

How do i differentiate a cosx function when x is in degrees? [migrated]

i have been having a hard trouble working on excercise 4a since i cannot understand how to differentiate a trig function that has x in degrees. How is it done? .
4
votes
2answers
655 views

Mathematica gives an unexpected answer for Integrate [closed]

I need to integrate the following: \begin{equation}\tag{1} \frac{\sqrt{C + (1 - C) x^3}}{x}, \end{equation} where $0 < C < 1$ and $x$ is a positive variable (then $x^3 \ge 0$). When I integrate:...
4
votes
1answer
54 views

Computing the seven roots of a polynomial

This question was originally asked by @fsrong70 six months ago. The OP deleted it shortly after posting and has not returned to this site since. I had just figured it out when it was deleted. I ...
3
votes
1answer
51 views

Simplifying symbolic integration with trigonometric functions

I am using DSolve to verify a multitude of definite integrals I have done by hand, and things have gone perfectly until this integral, $$ \int_0^t \frac{\mathrm{d}...
3
votes
4answers
186 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
0
votes
1answer
46 views

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: ...
1
vote
1answer
135 views

How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...
0
votes
1answer
84 views

Blood Pressure problem given equation [closed]

The blood pressure (P) of an individual after t seconds with a heart rate of 70 beats/min. can be modeled by the function, P(t) = 100 + 20 sin(7π/3)t In the time interval from 0s ...
0
votes
1answer
117 views

Trouble plotting P(t) = 100 + 20 sin(7π t/3) [closed]

I'm trying to plot this but I keep getting an empty graph. I put in: Plot[P[t_] := 100 + 20 sin[(7 pi)/3] t, {t, 0, 10}]
0
votes
1answer
76 views

I need to solve this equation: 2 cos^2 θ − 7 cos θ − 4 = 0 on the interval 0 ≤ θ < 2 π [closed]

I've been trying to solve the problem, but I keep getting errors.Thanks for the help.
1
vote
1answer
44 views

Solve command doesn't work (i'm beginner)

I try to perform the equation by writing: ...
0
votes
1answer
63 views

Interpretation of PolarPlot

I tried to plot the function $r=-2t$ with $t$ in $[0,2\pi]$: PolarPlot[-2 t, {t, 0, 2 Pi}, AxesLabel -> {x, y}] When $t=\pi/4$, I have: $$r=-\pi/2=-1.57$$ ...
0
votes
1answer
56 views

FullSimplify not simplifying expression containing the form Sin[n] where n is an integer [closed]

I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why? ...
3
votes
1answer
59 views

Generating trigonometric sums

How can one generate all cosine polynomials with $\pm1$ coefficient of following form: $$\sum_{k=1}^n\pm\cos kt.$$ I tried DO loop but couldn't get all of them as clearly cannot exhaust $2^n$ ...
2
votes
1answer
95 views

Domain and codomain of a function

I am wondering if it is possible to get domain and codomain of a function in Mathematica (by using only built-in functions if possible). For example, I would like to give as input the function $tan(x)$...
4
votes
4answers
246 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
3
votes
1answer
67 views

Given two lines find the four circles that have the lines as tangents

Given two lines, each defined by two points, and a radius find the four circles that have the lines as tangents. I give my attempt below but there ought to be a nice mathematica way of doing this. <...
0
votes
0answers
36 views
2
votes
2answers
128 views

Fourier Phase Angle Interpretation

I am trying to fit the following tide data (taken from here) with a sinusoidal curve that looks like the following: displacement+amplitude * sin(t w - ph), where t is the independent variable, w is ...
1
vote
1answer
47 views

Plot contour of zeroes against trig function

Take two functions: func1=Cos[Pi*x]*Cos[Pi*y] func2=x Sin[Pi*x] I want to create a plot that shows a 2D contour map of ...
1
vote
1answer
38 views

Strange output for solve in terms of trigonometric functions

I am using the following Solve code: ...
0
votes
1answer
62 views

Defined function doesn't plot correctly

I have defined a function that produces a single negative impulse spanning -b to -a and a positive impulse spanning ...
1
vote
1answer
64 views

Plot of integral of summed `Sinc` series is incorrect

I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy: ...
0
votes
1answer
65 views

Incorrect results in trig table

I have a table given by Table[ Evaluate[ Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]], {r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0 The ...
1
vote
1answer
41 views

Find closed form for roots of trig formula

I have the expression Sum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0 I want to find the roots in terms of ...
3
votes
2answers
91 views

Indefinite ArcTan integral does not return the (known) real expression but returns complex expression

I have a problem with an indefinite integral which I solved using MMA in back in 2010 (must have been version 7 or 8) successfullly and it gave an elegant result. However, if I run it with MMA 11.3 (...
3
votes
1answer
121 views

Indeterminate result from Sinc

I have an impulse train given by (1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R) Because of the Csc, ...
4
votes
1answer
64 views

Solve/Reduce not working on a function with a condition/domain restriction?

I'm working with a trigonometric function, so I thought it would be convenient to set a condition to restrict the domain so I wouldn't have to specify it in the solve function each time. Here is a ...
4
votes
1answer
87 views

Prevent Trigonometric simplifications from using double angle and half angle formulae?

Is there any way to force Mathematica to not use double and half angle formulae etc. when simplifying Trigonometric expressions? For example,...
2
votes
1answer
103 views

Convert trigonometric expression into other forms using just a specific set of identities

I am trying to convert a trigonometric expression like sinθ/(1 - cosθ) into cosecθ + cotθ or ...
1
vote
1answer
64 views

Why is this function indeterminate?

Consider an impulse train 1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1) For x=0 it's clear that this function ...
0
votes
2answers
102 views

How can I avoid the message Infinity::indet?

I have an impulse train of frequency R: 1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1) For ...
0
votes
2answers
36 views

Force a result from “Indeterminate” for single impulse?

The formula for a single impulse of amplitude $1$ at $x=r$ is given by $$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$ (In MathJax because it's a math formula.) Formally, at $x=r$, this function evaluates ...
1
vote
1answer
29 views

Trigonometric simplification with assumptions fails

Consider the following input Assuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...
0
votes
2answers
45 views

Plotting a function while varying a variable (on the x-axis) using two formulas [duplicate]

I want to plot the following function, where Rb is the variable (that has to be on the x-axis): ...
6
votes
1answer
252 views

Integral that yields ArcTan function rather than ArcSin

When I enter the following Integral problem to Mathematica, $$ \int \frac{1}{\sqrt{a²-x²}}\textrm{d}x $$ The answer yielded by Mathematica is $$ \arctan\left({\frac{x}{\sqrt{a²-x^2}}}\right) $$ Rather ...
1
vote
1answer
42 views

Not getting expected simplification of trigonometric expressions

I have two trigonometric expressions. I would like to eliminate the fraction from my 2nd expression. ...
1
vote
2answers
89 views

Solve trig equation

I have a simple trig equation: Clear[f, x] f[x_] = Cos[2*x] - 3 Sin[x] + 2 Solve[f[x] == 0, x] I received a very long a complicated reply that I do not ...
0
votes
1answer
84 views

Get the square root of a+bi,when a>0,b>0 in radical form

My code returns this result involves trigonometric functions, ...
1
vote
2answers
102 views
1
vote
1answer
97 views

Substitution in trigonometric expressions to remove secant and cosecant functions

I manipulate equations which are trigonometric equations in mechanics. In theses equations, the custom is to use only Cos, Sin and Tan functions and not the secant and cosecant functions. To prevent ...
0
votes
1answer
91 views

Verify solution of system of first order ODE

I am given a solution $v_1$(t)=$-e^{t/2}cost$ for a system of first order ODE and I am asked to verify this solution can solves the linear second order ODE in terms of $y_1$(t) Here is the matrix ...
0
votes
2answers
129 views

Trig function graphing exercise [closed]

I am trying to figure out how to do the following exercise in Mathematica Graph $y(t)= a \cos t + b \sin t - 0.5 \sin t$ on the interval $0 ≤ t ≤ 6\, π$
0
votes
1answer
60 views

Solving a trig equation in a specific range

I want to define a function as such g[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]] However the result comes out as a conditional expression, for ...
0
votes
1answer
34 views

How to get a single evaluation of RandomReal in a Block

I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]). The two ...
0
votes
0answers
87 views

User defined ArcTan function

I am trying to integrate an equation that requires an angle term calculated using ArcTan[x,y]. A number of issues have been mentioned about ...
1
vote
0answers
59 views

Determining the angle x through the point of intersection between lines in any triangle [closed]

I'm trying to determine the angle x in the triangle shown below. Given $\overline{DB}=\overline{DE}$ Given $\overline{AD}=\overline{DC}$ Given $\angle ADE=40^°$ Find $\angle DCB$ But I'm finding ...
2
votes
5answers
152 views

To solve this problem just follow this rule or is there another possibility?

To solve this problem just follow this rule or is there another possibility? Solve[(3 Sqrt[2])/Sin[60 Degree] == x/Sin[45 Degree], {x}]