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Questions tagged [trigonometry]

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

Use this tag for questions related to trigonometric and hyperbolic functions.

504 questions
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3 answers

Behavior of ArcTan when two zeros are given as arguments

I've noticed that the numeric approximation of ArcTan is a bit different from the symbolic one. If I write ArcTan[0,0] I obtain ArcTan::indet: "Indeterminate expression ArcTan[0,0] encountered. While if I write ArcTan[0.0, 0] I obtain 0 Instead…
Jepessen
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5
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Amplitude of a Sinus, Simple question

I have a rather simple question. I would like to find the Amplitude of a Sinus using mathematica: w=10; 5*Sin[w*t-2] The Amplitude is obviously 5. Now, what I tried was to first convert the Sinus into Exponential…
henry
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4
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1 answer

Eliminate 3 Variable from 4 Equations

I am trying to use Mathematica to Eliminate 3 following variable from 4 equations. Any clue or link to similar solved problem is highly appreciated: eq = { Cos[θ] + Cos[ϕ] + Cos[ψ] == a, Sin[θ] + Sin[ϕ] + Sin[ψ] == b, Cos[2 θ] + Cos[2 ϕ] +…
Max Jasper
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4
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2 answers

Sign change of sine function

I was trying to extract the parameter of the phase term of the sine function, and I found the problem that Mathamtica automatically try to change the sign of the sine function. I got negative number or positive amplitude from the sine function. I…
Saesun Kim
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4
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1 answer

Trigonometry and Solve

I'm trying to find values ​​for "x" using Solve, but I do not think it's the best solution. What is the most appropriate function to calculate this? Solve[Tan[α] == a/x && Tan[2 α] == (a + 5)/x && x^2 + (a + 5)^2 == 10^2, {x, a}]
user45104
4
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2 answers

Solving trig identities in specific terms

How would you solve a problem like "write csc(x) in terms of sec(x)" in Mathematica? The best I can get is "True." https://math.stackexchange.com/questions/167935/write-cscx-in-terms-of-secx I'm asking in order to better understanding of…
user2353
3
votes
1 answer

Sum to Product Trig Identities

All, I was enjoying sum to product trig identities in Mathematica, smiling that it was going well, producing the same answers trig students get by hand. Sin[α] + Sin[β] // TrigFactor Answer: 2 Cos[α/2 - β/2] Sin[α/2 + β/2] And my first…
David
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3
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1 answer

Mathematica's ArcTan function

I'm trying to calculate the angle made by a vector from two vector components but am having some trouble. The x-component has a magnitude of -2.7388321862151737*^10 and the y-component has a magnitude of 1.4452659458183087*^11. Now, using the ArcTan…
InquisitiveInquirer
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5 answers

How do you make Tan[A+B] expansion give the well known high school answer?

What command makes Tan[A+B] expand to (Tan[A]+Tan[B])/(1-Tan[A]Tan[B])? TrigExpand does not give it directly.
Quasar Supernova
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3
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2 answers

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 Sqrt[2]*Cos[-Pi/4 + x] Using ReplaceAll doesn't help, since it does the replacement,…
Andrey Kuzminskiy
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3
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2 answers

Two values of ArcCos not showing

When I try to find θ = ArcCos[-.5] I am expecting more than one answer: $$2 \pi/3, 4\pi/3,...$$ But Mathematica is returning only one: 2.0944 and it is not in angle format as well. Is there a way to get all the values of angles in angle format?
Jasmine
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1 answer

How to do some trigonometric derivations

Two substitutions fail, so do I forget some earlier steps? For Cos[x] == Sin[(1/2)*Pi + x] /. x -> (1/2)*x = true I don't get the final answer, but only true. Cos[(1/2)*x] == Sin[(1/2)*Pi + (1/2)*x] (final answer) A second derivation case…
janhardo
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2
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1 answer

Returning trigonometric value answers in irrational form

I need to find the irrational form of Sin[7*\[Pi]/8]. But in Mathematica, I can get its numerical value. I am getting Sin[\[Pi]/4]=1/Sqrt[2] in Mathematica. What I meant is an answer something like this for Sin[7*\[Pi]/8] as well. Is that…
Jasmine
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2
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1 answer

Solving simple trig equation

I tried to solve a simple trig equation. Solve[{Sin[x] == Cos[x], 0 <= x <= Pi}]; The answer should be pi/4 But I get simplify[{{x -> -2 ArcTan[1 - Sqrt[2]]}}]
smellerbee
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0 answers

Tangent of 2 times arc cosine of -3/4

Tan[ArcCos[-3/4] Returns the exact answer: -(Sqrt[7]/3) But: Tan[2 ArcCos[-3/4]] Does not return an exact answer. Any way to force it to return an exact answer?
David
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