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Mathematics 16 Online
OpenStudy (unklerhaukus):

\[\sin(1)=\]

OpenStudy (dls):

sin(1 degrees)=0.01745240643728351281941897851 sin(1 radians)=0.84147098480789650665250232163…

OpenStudy (unklerhaukus):

yuk

OpenStudy (dls):

You can approximate the sine of a small angle to arbitrary accuracy quite easily. First transform the number into radians by multiplying by pi/180. Then call the number x and sin(x) = x - x^3/3! +x^5/5! - x^7/7! and so on. If x = 1 degree, it turns out that by the time you've handled the term in x^5 the answer is accurate to about 1 part in 10^16. This should be accurate enough!

OpenStudy (unklerhaukus):

\[\sin(1) \approx 1 - 1/3! +1/5! - 1/7!\]\[\quad=1-1/6+1/120-1/5040\]\[=(5040-840+42-1)/5040\]\[=4241/5040\]

OpenStudy (unklerhaukus):

is it a transcendental number or not?

OpenStudy (unklerhaukus):

\[\sin(1)=\frac{ie^{-i}-ie^{i}}{2}\]

OpenStudy (unklerhaukus):

|dw:1345807761301:dw|

OpenStudy (anonymous):

its an irrational number but how about transcendental !!!

OpenStudy (unklerhaukus):

i dont get it/

OpenStudy (anonymous):

i mean \(\sin 1\) is irrational

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