Processing Math: Done

From Förberedande kurs i matematik 1

Revision as of 09:33, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 4.1:2 moved to Solution 4.1:2: Robot: moved page) ← Previous diff		Current revision (07:59, 3 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If we use the mnemonic that one turn is 360° or <math>2\pi</math> radians, we can derive a formula for the transformation from degrees to radians. Because
-	<center> [[Image:4_1_2.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>360\cdot 1^{\circ } = 2\pi\ \text{radians}</math>}}
		+
		+	this gives
		+
		+	{{Displayed math||<math>1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}</math>}}
		+
		+	Now we can start transforming the angles:
		+
		+
		+	{|
		+	||a)&nbsp;&nbsp;
		+	|width="100%"|<math>45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||b)&nbsp;&nbsp;
		+	|width="100%"|<math>135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||c)&nbsp;&nbsp;
		+	|width="100%"|<math>-63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,}</math>
		+	|-
		+	|height="10px"|&nbsp;
		+	|-
		+	||d)
		+	|width="100%"|<math>270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.}</math>
		+	|}

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Current revision

If we use the mnemonic that one turn is 360° or 2 radians, we can derive a formula for the transformation from degrees to radians. Because

3601=2 radians

this gives

1=2360 radians=180 radians.

Now we can start transforming the angles:

a)	45=451=45180 radians=4 radians,
b)	135=1351=135180 radians=43 radians,
c)	−63=−631=−63180 radians=−207 radians,
d)	270=2701=270180 radians=23 radians.