From Förberedande kurs i matematik 1

Revision as of 09:55, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 4.3:4d moved to Solution 4.3:4d: Robot: moved page) ← Previous diff		Current revision (14:16, 9 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	With the formula for double angles and the Pythagorean identity <math>\cos^2\!v + \sin^2\!v = 1</math>, we can express <math>\cos 2v</math> in terms of <math>\cos v</math>,
-	<center> [[Image:4_3_4d.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\begin{align}
		+	\cos 2v &= \cos^2\!v - \sin^2\!v\\[5pt]
		+	&= \cos^2\!v - (1-\cos^2\!v)\\[5pt]
		+	&= 2\cos^2\!v-1\\[5pt]
		+	&= 2b^2-1\,\textrm{.}
		+	\end{align}</math>}}

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Current revision

With the formula for double angles and the Pythagorean identity \displaystyle \cos^2\!v + \sin^2\!v = 1, we can express \displaystyle \cos 2v in terms of \displaystyle \cos v,

\displaystyle \begin{align} \cos 2v &= \cos^2\!v - \sin^2\!v\\[5pt] &= \cos^2\!v - (1-\cos^2\!v)\\[5pt] &= 2\cos^2\!v-1\\[5pt] &= 2b^2-1\,\textrm{.} \end{align}