Appendix/Ramblings/TrigFunctions - Revision history

Jet53man: /* Integer-Degree Angles */

2022-04-07T00:55:36Z

Integer-Degree Angles

← Older revision		Revision as of 20:55, 6 April 2022
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	==Integer-Degree Angles==		==Integer-Degree Angles==

	A PDF-formatted document generated by James T. Parent lists [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf exact values for the sine of all integer-degree angles] between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the [https://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212 ''SquareCirclez'' IntMath blog].		A PDF-formatted document generated by James T. Parent<sup>&dagger;</sup> lists [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf exact values for the sine of all integer-degree angles] between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the [https://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212 ''SquareCirclez'' IntMath blog].


	<table border="1" align="center" cellpadding="8">		<table border="1" align="center" cellpadding="8" width="75%">
	<tr>		<tr>
	<td align="center" colspan="3">Examples Extracted from the [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf James T. Parent Document]</td>		<td align="center" colspan="3">Examples Extracted from the [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf James T. Parent Document]<sup>&dagger;</sup></td>
	</tr>		</tr>

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	<td align="center"><math>75^\circ</math></td>		<td align="center"><math>75^\circ</math></td>
	<td align="center"><math>\frac{\sqrt{3} + 1}{2\sqrt{2}}</math></td>		<td align="center"><math>\frac{\sqrt{3} + 1}{2\sqrt{2}}</math></td>
			</tr>

			<tr>
			<td align="left" colspan="3">
			<sup>&dagger;</sup>James T. Parent has previously taught mathematics at Schenectady County Community College, Schenectady, New York, and at Great Bay Community College, Portsmouth, New Hampshire.
			</td>
	</tr>		</tr>
	</table>		</table>

Jet53man: /* Integer-Degree Angles */

2022-04-06T17:55:58Z

Integer-Degree Angles

← Older revision		Revision as of 13:55, 6 April 2022
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	<td align="center">		<td align="center">
	<math>		<math>
			\frac{\sqrt{2}}{4}\biggl( \sqrt{3} - 1\biggr)
			=
	\frac{1}{2}\biggl(2 - \sqrt{3}\biggr)^{1 / 2}		\frac{1}{2}\biggl(2 - \sqrt{3}\biggr)^{1 / 2}
	</math>		</math>
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	<td align="center">		<td align="center">
	<math>		<math>
			\frac{\sqrt{2}}{8} \biggl( \sqrt{5} - 1\biggr) \biggl( 5 + \sqrt{5} \biggr)^{ 1 /2}
			=
	\frac{1}{4}\biggl(10 - 2\sqrt{5}\biggr)^{1 / 2}		\frac{1}{4}\biggl(10 - 2\sqrt{5}\biggr)^{1 / 2}
	</math>		</math>

Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

2022-04-06T17:45:44Z

Analytic Expressions for Selected Trigonometric Functions

← Older revision		Revision as of 13:45, 6 April 2022
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	A PDF-formatted document generated by James T. Parent lists [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf exact values for the sine of all integer-degree angles] between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the [https://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212 ''SquareCirclez'' IntMath blog].		A PDF-formatted document generated by James T. Parent lists [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf exact values for the sine of all integer-degree angles] between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the [https://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212 ''SquareCirclez'' IntMath blog].


			<table border="1" align="center" cellpadding="8">
			<tr>
			<td align="center" colspan="3">Examples Extracted from the [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf James T. Parent Document]</td>
			</tr>

			<tr>
			<td align="center" colspan="2"><math>0 \le</math> Angle <math>(\theta) \le \frac{\pi}{2}</math></td>
			<td align="center" rowspan="2"><math>\sin\theta</math></td>
			</tr>
			<tr>
			<td align="center">Radians</td>
			<td align="center">Degrees</td>
			</tr>

			<tr>
			<td align="center"><math>\frac{\pi}{60}</math></td>
			<td align="center"><math>3^\circ</math></td>
			<td align="center">
			<math>
			\frac{\sqrt{6}}{48} \biggl(\sqrt{5} - 1\biggr)\biggl(3 + \sqrt{3}\biggr)
			- \frac{\sqrt{3}}{24}\biggl(3 - \sqrt{3}\biggr)\biggl(5 + \sqrt{5}\biggr)^{1 / 2}
			</math>
			</td>
			</tr>

			<tr>
			<td align="center"><math>\frac{\pi}{12}</math></td>
			<td align="center"><math>15^\circ</math></td>
			<td align="center">
			<math>
			\frac{1}{2}\biggl(2 - \sqrt{3}\biggr)^{1 / 2}
			</math>
			</td>
			</tr>

			<tr>
			<td align="center"><math>\frac{\pi}{5}</math></td>
			<td align="center"><math>36^\circ</math></td>
			<td align="center">
			<math>
			\frac{1}{4}\biggl(10 - 2\sqrt{5}\biggr)^{1 / 2}
			</math>
			</td>
			</tr>

			<tr>
			<td align="center"><math>\frac{5\pi}{12}</math></td>
			<td align="center"><math>75^\circ</math></td>
			<td align="center"><math>\frac{\sqrt{3} + 1}{2\sqrt{2}}</math></td>
			</tr>
			</table>


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Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

2022-04-06T17:17:29Z

Analytic Expressions for Selected Trigonometric Functions

← Older revision		Revision as of 13:17, 6 April 2022
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	</tr>		</tr>
	</table>		</table>

			==Integer-Degree Angles==

			A PDF-formatted document generated by James T. Parent lists [https://www.intmath.com/blog/wp-content/images/2011/06/exact-values-sin-degrees.pdf exact values for the sine of all integer-degree angles] between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the [https://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212 ''SquareCirclez'' IntMath blog].



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Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

2022-04-06T16:45:54Z

Analytic Expressions for Selected Trigonometric Functions

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2022-04-06T16:07:31Z

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Appendix/Ramblings/TrigFunctions - Revision history

Jet53man: /* Integer-Degree Angles */

Jet53man: /* Integer-Degree Angles */

Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

Jet53man: /* Analytic Expressions for Selected Trigonometric Functions */

Jet53man: Created page with "__FORCETOC__ =Analytic Expressions for Selected Trigonometric Functions= {{ SGFfooter }}"

Jet53man: Created page with "FORCETOC =Analytic Expressions for Selected Trigonometric Functions= {{ SGFfooter }}"