Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Solution 4.3:4f

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 4.3:4f moved to Solution 4.3:4f: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
Using the addition formula for cosine, we can express
-
<center> [[Image:4_3_4f.gif]] </center>
+
<math>\cos \left( v-{\pi }/{3}\; \right)</math>
-
{{NAVCONTENT_STOP}}
+
in terms of
 +
<math>\text{cos }v</math>
 +
and
 +
<math>\text{sin }v</math>,
 +
 
 +
 
 +
<math>\cos \left( v-\frac{\pi }{3} \right)=\cos v\centerdot \cos \frac{\pi }{3}+\sin v\centerdot \sin \frac{\pi }{3}</math>
 +
 
 +
 
 +
Since
 +
<math>\text{cos }v=b\text{ }</math>
 +
and
 +
<math>\sin v=\sqrt{1-b^{2}}</math>
 +
we obtain
 +
 
 +
 
 +
<math>\cos \left( v-\frac{\pi }{3} \right)=b\centerdot \frac{1}{2}+\sqrt{1-b^{2}}\centerdot \frac{\sqrt{3}}{2}</math>

Revision as of 12:00, 29 September 2008

Using the addition formula for cosine, we can express cosv−3  in terms of cos v and sin v,


cosv−3=cosvcos3+sinvsin3 


Since cos v=b and sinv=1−b2  we obtain


cosv−3=b21+1−b223 

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_4.3:4f"