8.5.2 Greatest hits from previous weeks

8.5.2.1 How to express trigonometric equation in terms of of given trigonometric function?
8.5.2.2 What is the difference between Reduce and Solve?
8.5.2.3 How to make the digits of  go around in a spiral like this?
8.5.2.4 Elegant operations on matrix rows and columns
8.5.2.5 Finding unit tangent, normal, and binormal vectors for a given r(t)
8.5.2.6 How to plot an ellipse?
8.5.2.7 Plotting Complex Quantity Functions
8.5.2.1 How to express trigonometric equation in terms of of given trigonometric function?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=434

How can I express a trigonometric equation / identity in terms of a given trigonometric function? 
 
using following trigonometric identities 
 
... 
[functions] [trigonometry]
 
asked by Prashant Bhate https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=99 Score of 30
answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 Score of 37
8.5.2.2 What is the difference between Reduce and Solve?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=17127

 Solve  and  Reduce  both can be used for solving equations. 
 
Just by working with them, I know there are some differences between ... 
[equation-solving] [functions] [function-comparison]
 
asked by lachis83 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2371 Score of 105
8.5.2.3 How to make the digits of  go around in a spiral like this?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=109982

Here is a start. 
 
 MapIndexed[Text[Reverse[First[RealDigits[Pi,10,252]]][[Tr@#2]],#]&, 
Table[{t Cos[t],t Sin[t]},{t,0,16Pi,0.2}]]//Graphics 
 
[graphics] [formatting] [generative-art]
 
asked by matrix89 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 Score of 57
answered by Martin Ender https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2305 Score of 73
8.5.2.4 Elegant operations on matrix rows and columns

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3069

Question 
 
The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ... 
[list-manipulation] [matrix] [array] [faq]
 
asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 Score of 191
answered by Mr.Wizard https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=121 Score of 63
8.5.2.5 Finding unit tangent, normal, and binormal vectors for a given r(t)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18598

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. 
 
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ... 
[equation-solving] [calculus-and-analysis] [geometry] [vector-calculus] [homework]
 
asked by a98 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5605 Score of 32
answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 Score of 47
8.5.2.6 How to plot an ellipse?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=20100

I'm new to Mathematica, and I'm finding it difficult to plot an ellipse. 
I tried using 
 
 Plot[(x/5)^2 + (y/3)^2 == 1, {x, -5, 5}, {y, -3, 3}] 
 
 
but I'm getting ... 
[plotting]
 
asked by Sriram https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=6075 Score of 18
answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 Score of 31
8.5.2.7 Plotting Complex Quantity Functions

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3458

Trying to plot with complex quantities seems not to work properly in what I want to accomplish. I would like to know if there is a general rule/way of plotting when you have complex counterparts in ... 
[plotting] [complex] [faq]
 
asked by night owl https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=116 Score of 42
answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 Score of 29