From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	With the help of the Pythagorean identity, we can express <math>\cos v</math> in terms of <math>\sin v</math>,
-	<center> [[Bild:4_3_3c.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\cos^2 v + \sin^2 v = 1\qquad\Leftrightarrow\qquad \cos v = \pm\sqrt{1-\sin^2 v}\,\textrm{.}</math>}}
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		+	In addition, we know that the angle <math>v</math> lies between <math>-\pi/2</math>
		+	and <math>\pi/2</math>, i.e. either in the first or fourth quadrant, where angles always have a positive ''x''-coordinate (cosine value); thus, we can conclude that
		+
		+	{{Displayed math||<math>\cos v = \sqrt{1-\sin^2 v} = \sqrt{1-a^2}\,\textrm{.}</math>}}

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Current revision

With the help of the Pythagorean identity, we can express \displaystyle \cos v in terms of \displaystyle \sin v,

\displaystyle \cos^2 v + \sin^2 v = 1\qquad\Leftrightarrow\qquad \cos v = \pm\sqrt{1-\sin^2 v}\,\textrm{.}

In addition, we know that the angle \displaystyle v lies between \displaystyle -\pi/2 and \displaystyle \pi/2, i.e. either in the first or fourth quadrant, where angles always have a positive x-coordinate (cosine value); thus, we can conclude that

\displaystyle \cos v = \sqrt{1-\sin^2 v} = \sqrt{1-a^2}\,\textrm{.}