Anyone out there can solve this equation ?
sin(80)/sin(40)=sin(160-x)/sin(x)
Here is the solution from Wolfram
Quote: teliotAssuming degrees (and converting to radians),
Here is the solution from Wolfram
I did it by hand. I got the same result.
Quote: teliotAssuming degrees (and converting to radians),
Here is the solution from Wolfram
Went. Looked. Awesome. But, also, "how do you cure hiccups" is showing as a related search. I remember being told in highschool that trig was like magic. But, really now...?
Quote: teliotAssuming degrees (and converting to radians),
Here is the solution from Wolfram
So, what is the answer ?
x=30 ?? :=)
If you want an approximate answer, use the fact that Sin(x) is about equal to x - x^3/6, plug in your values and solve the cubic. (But, convert to radians first.)Quote: ssho88Quote: teliotAssuming degrees (and converting to radians),
Here is the solution from Wolfram
So, what is the answer ?
x=30 ?? :=)
Visually looking at the graph, it looks like about 2.8 radians, which is about equal to 160 degrees, oddly.Quote: ssho88So, what is the answer ? x=30 ?? :=)
Quote: teliotIf you want an approximate answer, use the fact that Sin(x) is about equal to x - x^3/6, plug in your values and solve the cubic. (But, convert to radians first.)Quote: ssho88Quote: teliotAssuming degrees (and converting to radians),
Here is the solution from Wolfram
So, what is the answer ?
x=30 ?? :=)
How to prove that x=30(degrees) ?
If you just use Sin(A-B) = Sin(A)Cos(B) - Sin(B)Cos(A) you easily get an answer involving arctan. I probably made an error, but what I got wasQuote: ssho88I want the exact answer
arctan(Sin(160)/[(Sin(80)/Sin(40)) + Cos(160)])
In my opinion, that is an exact answer.
Quote: teliotIf you just use Sin(A-B) = Sin(A)Cos(B) - Sin(B)Cos(A) you easily get an answer involving arctan. I probably made an error, but what I got was
arctan(Sin(160)/[(Sin(80)/Sin(40)) + Cos(160)])
In my opinion, that is an exact answer.
I have simplified it to, tan(x) = sin(20)/[2*cos(40)-cos(20)]
x= arctan(sin(20)/[2*cos(40)-cos(20)]) ?
FWIW, the source's instructions (but not the instructions in the puzzle thread) say NOT to use trig, and to use geometry instead.
Quote: ssho88So, what is the answer ?
Who cares. This is the math forum. It is sufficient that an answer exists and is unique. Furthermore WolframAlpha gives you an exact expression... who would you ever need more ? :)
Quote: rdw4potusIndeed. And the solution to this formula is "supposed to be" 30 degrees, so that it validates the trig-based answer to the puzzle.
FWIW, the source's instructions (but not the instructions in the puzzle thread) say NOT to use trig, and to use geometry instead.
Could you please show me the source's instructions ?
Quote: ssho88Could you please show me the source's instructions ?
You may use only elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use trigonomery, such as sines and cosines, the law of sines, the law of cosines, etc.]
Quote: rdw4potus
Thanks. Trigonometry can solve both problem 1 and 2 !
