From Förberedande kurs i matematik 1

Revision as of 12:27, 3 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:4_4_2c.gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (14:25, 10 October 2008) (edit) (undo) Tek (Talk | contribs) m
(4 intermediate revisions not shown.)
Line 1:		Line 1:
-	{{NAVCONTENT_START}}	+	There are two angles in the unit circle, <math>x=0</math> and <math>x=\pi</math>, whose sine has a value of zero.
-	<center> [[Bild:4_4_2c.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	[[Image:4_4_2_c.gif|center]]
		+
		+	We get the full solution when we add multiples of <math>2\pi</math>,
		+
		+	{{Displayed math||<math>x = 0+2n\pi\qquad\text{and}\qquad x = \pi + 2n\pi\,,</math>}}
		+
		+	where ''n'' is an arbitrary integer.
		+
		+
		+	Note: Because the difference between <math>0</math> and <math>\pi</math> is a half turn, the solutions are repeated every half turn and they can be summarized in one expression,
		+
		+	{{Displayed math||<math>x=0+n\pi\,,</math>}}
		+
		+	where ''n'' is an arbitrary integer.

---

Current revision

There are two angles in the unit circle, \displaystyle x=0 and \displaystyle x=\pi, whose sine has a value of zero.

We get the full solution when we add multiples of \displaystyle 2\pi,

\displaystyle x = 0+2n\pi\qquad\text{and}\qquad x = \pi + 2n\pi\,,

where n is an arbitrary integer.

Note: Because the difference between \displaystyle 0 and \displaystyle \pi is a half turn, the solutions are repeated every half turn and they can be summarized in one expression,

\displaystyle x=0+n\pi\,,

where n is an arbitrary integer.