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How to find the sine/cos/tangent/cotangent/cossec/sec of an angle:

In degrees

$\sin(23^{\circ}) =$ ?

In radians

$\sin(0.53) =$ ?

apnorton
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Fabricio
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  • What is the relationship between $\sin(x)$ and $\cos(x)$? Now given them both, what is $\tan(x)$ and $\cot(x)$? Ditto $\sec(x)$ and $\csc(x)$... – gt6989b Jun 07 '13 at 20:01
  • To understand the relationship between $\sin x$ and $\cos x$, think about a common identity they satisfy. – gt6989b Jun 07 '13 at 20:02
  • Do you want an exact form, or a way to find the result to an arbitrary number of decimal places? (Taylor expansion could help) – apnorton Jun 07 '13 at 20:04
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    To get the value approximately, note that $23 \approx 22.5 = 45/2$. Since you know all functions of 45 degrees, you can now approximate – gt6989b Jun 07 '13 at 20:04

1 Answers1

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In radians you can use the power series of the sine function to get very close to the true value. $$\sin (x) = x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-\frac{x^{11}}{11!}+\cdots$$

The remaining functions have their own power series representations which can be used as well.

Wintermute
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