Solution 4.4:1d

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.4:1d moved to Solution 4.4:1d: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
Because
-
<center> [[Image:4_4_1d.gif]] </center>
+
<math>\tan v=\frac{\sin v}{\cos v}</math>, the condition
-
{{NAVCONTENT_STOP}}
+
<math>\text{tan }v=\text{1 }</math>
 +
gives
 +
<math>\text{sin }v=\text{ cos }v</math>, i.e. we look for angles in the unit circle whose
 +
<math>x</math>
 +
- and
 +
<math>y</math>
 +
-coordinates are equal.
 +
 
 +
After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions,
 +
<math>v={\pi }/{4}\;</math>
 +
and
 +
<math>v=\pi +{\pi }/{4}\;={5\pi }/{4}\;</math>
 +
 
 +
 
[[Image:4_4_1_d.gif|center]]
[[Image:4_4_1_d.gif|center]]

Revision as of 12:38, 30 September 2008

Because \displaystyle \tan v=\frac{\sin v}{\cos v}, the condition \displaystyle \text{tan }v=\text{1 } gives \displaystyle \text{sin }v=\text{ cos }v, i.e. we look for angles in the unit circle whose \displaystyle x - and \displaystyle y -coordinates are equal.

After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, \displaystyle v={\pi }/{4}\; and \displaystyle v=\pi +{\pi }/{4}\;={5\pi }/{4}\;



Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.4:1d"