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mathdad
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Evaluate sin 6 without using a calculator? How is this done?
Unit circle?
Unit circle?
topsquark said:I would imagine that 6 is in degrees. So instead of using 2 pi you would use 360.
-Dan
RTCNTC said:Yes, I meant evaluate sin(6°).
Can the unit circle be used?
convert(sin(Pi/30), radical)
MarkFL said:According to W|A:
\(\displaystyle \sin\left(6^{\circ}\right)=\frac{\sqrt{6(5-\sqrt{5})}-(1+\sqrt{5})}{8}\)
RTCNTC said:How did you arrive at this very impressive value for sin(6°)?
RTCNTC said:How did you arrive at this very impressive value for sin(6°)?
MarkFL said:Using W|A (wolframalpha.com)
RTCNTC said:I heard about wolfram. Who is the creator of wolfram?
MarkFL said:I don't know...the guy who introduced it to me shortly after I got involved in the online math communities told me it was "google for nerds." :)
MarkFL said:Using W|A (wolframalpha.com)
RTCNTC said:I am in the trigonometry sections of the David Cohen book. Should I post my questions in the MHB trigonometry forum or continue posting here?
RTCNTC said:I heard about wolfram. Who is the creator of wolfram?
That is not entirely true.Joppy said:Stephen Wolfram is the creator of WolframAlpha. His arrogance is unparalleled...
MarkFL said:According to W|A:
\(\displaystyle \sin\left(6^{\circ}\right)=\frac{\sqrt{6(5-\sqrt{5})}-(1+\sqrt{5})}{8}\)
kaliprasad said:$6^\circ= \frac{\pi}{5}-\frac{\pi}{6}$ and sin and cos for these values are computable and hence well known and can be used to compute
Krylov said:
RTCNTC said:Everyone has been so kind to me in terms of this question. Thank you.
RTCNTC said:- - - Updated - - -
Hope I did not start a war here. I have been curious about the wolfram site for years.
To evaluate sin 6 without using a calculator, you can use the Taylor series expansion of sin(x) = x - x^3/3! + x^5/5! - ..., where x is in radians. By plugging in 6 for x and performing the calculations, you can find the approximate value of sin 6.
Evaluating sin 6 without a calculator can help build a better understanding of trigonometric functions and their properties. It also allows for a more precise calculation, as calculators often round off decimal values.
No, since the Taylor series expansion of sin(x) is based on radians, you cannot use a calculator to directly evaluate sin 6 in degrees. You would first need to convert 6 degrees to radians by multiplying it by π/180.
The most accurate method is to use the Maclaurin series expansion of sin(x) = x - x^3/3! + x^5/5! - ..., where x is in radians, but this may require more terms to be calculated. Another accurate method is to use a trigonometric identity, such as sin(a+b) = sin(a)cos(b) + cos(a)sin(b), to reduce the angle to a value that is easier to work with, such as sin 6 = sin 5(cos 1) + cos 5(sin 1).
Yes, there are other methods such as using a unit circle, geometric constructions, or interpolation techniques. However, these methods may require more time and effort compared to using the Taylor series or trigonometric identities.