From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	We draw an angle <math>v</math> in the unit circle, and the fact that <math>\sin v = 3/10</math> means that its ''y''-coordinate equals <math>3/10</math>.
-	<center> [[Bild:4_3_6b-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+
-	{{NAVCONTENT_START}}	+
-	<center> [[Bild:4_3_6b-2(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+
-	[[Bild:4_3_6_b1.gif|center]]	+	[[Image:4_3_6_b1.gif|center]]
-	[[Bild:4_3_6_b2.gif|center]]	+	With the information that is given, we can define a right-angled triangle in the second quadrant which has a hypotenuse of 1 and a vertical side of length 3/10.
		+
		+	[[Image:4_3_6_b2.gif|center]]
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		+	We can determine the triangle's remaining side by using the Pythagorean theorem,
		+
		+	{{Displayed math||<math>a^2 + \Bigl(\frac{3}{10}\Bigr)^2 = 1^2</math>}}
		+
		+	which gives that
		+
		+	{{Displayed math||<math>a = \sqrt{1-\Bigl(\frac{3}{10}\Bigr)^2} = \sqrt{1-\frac{9}{100}} = \sqrt{\frac{91}{100}} = \frac{\sqrt{91}}{10}\,\textrm{.}</math>}}
		+
		+	This means that the angle's ''x''-coordinate is <math>-a</math>, i.e. we have
		+
		+	{{Displayed math||<math>\cos v=-\frac{\sqrt{91}}{10}</math>}}
		+
		+	and thus
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		+	{{Displayed math||<math>\tan v = \frac{\sin v}{\cos v} = \frac{\dfrac{3}{10}}{-\dfrac{\sqrt{91}}{10}} = -\frac{3}{\sqrt{91}}\,\textrm{.}</math>}}

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Current revision

We draw an angle \displaystyle v in the unit circle, and the fact that \displaystyle \sin v = 3/10 means that its y-coordinate equals \displaystyle 3/10.

With the information that is given, we can define a right-angled triangle in the second quadrant which has a hypotenuse of 1 and a vertical side of length 3/10.

We can determine the triangle's remaining side by using the Pythagorean theorem,

\displaystyle a^2 + \Bigl(\frac{3}{10}\Bigr)^2 = 1^2

which gives that

\displaystyle a = \sqrt{1-\Bigl(\frac{3}{10}\Bigr)^2} = \sqrt{1-\frac{9}{100}} = \sqrt{\frac{91}{100}} = \frac{\sqrt{91}}{10}\,\textrm{.}

This means that the angle's x-coordinate is \displaystyle -a, i.e. we have

\displaystyle \cos v=-\frac{\sqrt{91}}{10}

and thus

\displaystyle \tan v = \frac{\sin v}{\cos v} = \frac{\dfrac{3}{10}}{-\dfrac{\sqrt{91}}{10}} = -\frac{3}{\sqrt{91}}\,\textrm{.}