The mathematician formerly known as DayLateDon

1d
comment Evaluate trig functions without a calculator
@user163862: I'm really big on concepts myself, so when you get a chance, please edit your question (or post an answer!) with your teacher's explanation of what techniques you were expected to apply to the problem. If there's a conceptual approach that's able to resolve a 0.058 variation in the values, then I want to know what it is! :)
1d
comment How to find the radius of this middle circle arranged as shown.
@user71346: The new image should make things clear.
1d
revised How to find the radius of this middle circle arranged as shown.
New image makes symmetry clear.
2d
answered Evaluate trig functions without a calculator
2d
comment How to find the radius of this middle circle arranged as shown.
@user71346: The red-edged triangle is isosceles because the (entire) figure is symmetric across the "diagonal" line $\overleftrightarrow{OP}$, where $O$ is the center of the target circle, and $P$ is the midpoint of that triangle's hypotenuse.
2d
revised How to find the radius of this middle circle arranged as shown.
edited body
2d
answered How to find the radius of this middle circle arranged as shown.
2d
answered simplification of the area of a hyperbolic circle (BONOLA, S 53)
Aug
26
awarded Nice Answer
Aug
26
awarded Curious
Aug
25
comment In a triangle ABC, (b + c) cos A + (c + a) cos B + (a + b) cos C is equal to
I believe your second term should be "$(c+a)\cos B$".
Aug
25
comment In a triangle ABC, (b + c) cos A + (c + a) cos B + (a + b) cos C is equal to
Since you know the Law of Cosines, you can replace $\cos A$, $\cos B$, $\cos C$ in the expression with fractions involving $a$, $b$, $c$, then expand like crazy, and finally find that the result is pretty simple. (There's also far simpler approach.)
Aug
25
comment Why do these fractions give $99...9$?
This "splitting into half" stuff can be looked-at a little differently. If $x=0.\overline{abcdef}$, then $10^3x = abc.\overline{defabc}$, so that $(1+10^3)x = abc.\overline{[a+d][b+e][c+f]}$, where $[m+n]$ is a single digit (so, I'm assuming no "carries" here); that is, the repeating part of $(1+10^3)x$ is what you get by adding the "halves" of the repeating part of $x$. That you get $999$ as the sum of these halves says that $(1+10^3)x$ is an integer; namely $abc.\overline{999} = abc+1$. (In particular, $1001\cdot\frac{1}{13}=77=076+1$.)
Aug
25
asked Given two lists of similar orthogonal matrices with common "conjugator", determine that conjugator
Aug
24
revised Hyperbola like on a sphere
added 46 characters in body
Aug
24
comment Why $\cos^2 x-\sin^2 x = \cos 2x\;?$
@Paul: Very often, it seems that the hardest part of Calculus is the Pre-Calculus. :)
Aug
23
revised Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.
[Edit removed during grace period]
Aug
23
comment Do you paragraph a proof?
See Knuth/Larrabee/Roberts' "Mathematical Writing".
Aug
23
answered Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.
Aug
23
revised Divison of Fractions
edited tags; edited title
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