4.4 Övningar - Versionshistorik

KTH.SE:u1rp004j den 31 maj 2007 kl. 07.05

2007-05-31T07:05:20Z

← Äldre version		Versionen från 31 maj 2007 kl. 07.05
Rad 1:		Rad 1:
-	__NOTOC__	+
	==Övning 4.4:1==		==Övning 4.4:1==
	<div class="ovning">		<div class="ovning">

Tek den 15 maj 2007 kl. 14.41

2007-05-15T14:41:18Z

← Äldre version		Versionen från 15 maj 2007 kl. 14.41
Rad 6:		Rad 6:
	<tr align="left">		<tr align="left">
	<td class="ntext">a)</td>		<td class="ntext">a)</td>
-	<td class="ntext" width="33%">$\sin{v}=\displaystyle \frac{1}{2}$</td>	+	<td class="ntext" width="50%">$\sin{v}=\displaystyle \frac{1}{2}$</td>
	<td class="ntext">b)</td>		<td class="ntext">b)</td>
-	<td class="ntext" width="33%">$\cos{v}=\displaystyle \frac{1}{2}$</td>	+	<td class="ntext" width="50%">$\cos{v}=\displaystyle \frac{1}{2}$</td>
-	<td class="ntext">c)</td>	+
-	<td class="ntext" width="33%">$\sin{v}=1$</td>	+
	</tr>		</tr>
	<tr align="left">		<tr align="left">
		+	<td class="ntext">c)</td>
		+	<td class="ntext" width="50%">$\sin{v}=1$</td>
	<td class="ntext">d)</td>		<td class="ntext">d)</td>
-	<td class="ntext" width="33%">$\tan{v}=1$</td>	+	<td class="ntext" width="50%">$\tan{v}=1$</td>
		+	</tr>
		+	<tr align="left">
	<td class="ntext">e)</td>		<td class="ntext">e)</td>
-	<td class="ntext" width="33%">$\cos{v}=2$</td>	+	<td class="ntext" width="50%">$\cos{v}=2$</td>
	<td class="ntext">f)</td>		<td class="ntext">f)</td>
-	<td class="ntext" width="33%">$\sin{v}=-\displaystyle \frac{1}{2}$</td>	+	<td class="ntext" width="50%">$\sin{v}=-\displaystyle \frac{1}{2}$</td>
	</tr>		</tr>
	<tr align="left">		<tr align="left">
	<td class="ntext">g)</td>		<td class="ntext">g)</td>
-	<td class="ntext" width="33%">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td>	+	<td class="ntext" width="50%">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
Rad 35:		Rad 37:
	<tr align="left">		<tr align="left">
	<td class="ntext">a)</td>		<td class="ntext">a)</td>
-	<td class="ntext" width="33%">$\displaystyle v=\frac{\pi}{6},\ \displaystyle v=\frac{5\pi}{6}$</td>	+	<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{6}\,$, $\,\displaystyle v=\frac{5\pi}{6}$</td>
	<td class="ntext">b)</td>		<td class="ntext">b)</td>
-	<td class="ntext" width="33%">$\displaystyle v=\frac{\pi}{3},\ \displaystyle v=\frac{5\pi}{3}$</td>	+	<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$</td>
-	<td class="ntext">c)</td>	+
-	<td class="ntext" width="33%">$\displaystyle v=\frac{\pi}{2}$</td>	+
	</tr>		</tr>
	<tr align="left">		<tr align="left">
		+	<td class="ntext">c)</td>
		+	<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{2}$</td>
	<td class="ntext">d)</td>		<td class="ntext">d)</td>
-	<td class="ntext" width="33%">$\displaystyle v=\frac{\pi}{4},\ \displaystyle v=\frac{5\pi}{4}$</td>	+	<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{4}\,$, $\,\displaystyle v=\frac{5\pi}{4}$</td>
		+	</tr>
		+	<tr align="left">
	<td class="ntext">e)</td>		<td class="ntext">e)</td>
-	<td class="ntext" width="33%">lösning saknas</td>	+	<td class="ntext" width="50%">lösning saknas</td>
	<td class="ntext">f)</td>		<td class="ntext">f)</td>
-	<td class="ntext" width="33%">$\displaystyle v=\frac{11\pi}{6},\ \displaystyle v=\frac{7\pi}{6}$</td>	+	<td class="ntext" width="50%">$\displaystyle v=\frac{11\pi}{6}\,$, $\,\displaystyle v=\frac{7\pi}{6}$</td>
	</tr>		</tr>
	<tr align="left">		<tr align="left">
	<td class="ntext">g)</td>		<td class="ntext">g)</td>
-	<td class="ntext" width="50%">$\displaystyle v=\frac{5\pi}{6},\ \displaystyle v=\frac{11\pi}{6}$</td>	+	<td class="ntext" width="50%">$\displaystyle v=\frac{5\pi}{6}\,$, $\,\displaystyle v=\frac{11\pi}{6}$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>

Tek: En del ändringar

2007-05-15T14:24:52Z

En del ändringar

(Skillnad mellan versioner)

Ossiang: /* Övning 4.4:1 */

2007-04-30T17:03:49Z

Övning 4.4:1

← Äldre version		Versionen från 30 april 2007 kl. 17.03
Rad 1:		Rad 1:
-	==Övning 4.4:1==	+	==Övning 4.4:1==
	<div class="ovning">		<div class="ovning">
	För vilka vinklar $v$, där $0 \leq v\leq 2\pi$, gäller att		För vilka vinklar $v$, där $0 \leq v\leq 2\pi$, gäller att
	<table width="100%" cellspacing="10px">		<table width="100%" cellspacing="10px">
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">$\sin{v}=\displaystyle \frac{1}{2}$</td>		<td class="ntext">$\sin{v}=\displaystyle \frac{1}{2}$</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">$\cos{v}=\displaystyle \frac{1}{2}$</td>		<td class="ntext">$\cos{v}=\displaystyle \frac{1}{2}$</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">$\sin{v}=1$</td>		<td class="ntext">$\sin{v}=1$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{d) }$</td>	+	<td class="ntext">d)</td>
	<td class="ntext">$\tan{v}=1$</td>		<td class="ntext">$\tan{v}=1$</td>
-	<td class="ntext">$\textrm{e) }$</td>	+	<td class="ntext">e)</td>
	<td class="ntext">$\cos{v}=2$</td>		<td class="ntext">$\cos{v}=2$</td>
-	<td class="ntext">$\textrm{f) }$</td>	+	<td class="ntext">f)</td>
	<td class="ntext">$\sin{v}=-\displaystyle \frac{1}{2}$</td>		<td class="ntext">$\sin{v}=-\displaystyle \frac{1}{2}$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{g) }$</td>	+	<td class="ntext">g)</td>
	<td class="ntext">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td>		<td class="ntext">$\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}$</td>
	<td class="ntext"></td>		<td class="ntext"></td>
Rad 39:		Rad 39:
	<table width="100%" cellspacing="10px">		<table width="100%" cellspacing="10px">
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">$\displaystyle v=\frac{\pi}{6}, \displaystyle v=\frac{5\pi}{6}$</td>		<td class="ntext">$\displaystyle v=\frac{\pi}{6}, \displaystyle v=\frac{5\pi}{6}$</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">$\displaystyle v=\frac{\pi}{3}, \displaystyle v=\frac{5\pi}{3}$</td>		<td class="ntext">$\displaystyle v=\frac{\pi}{3}, \displaystyle v=\frac{5\pi}{3}$</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">$\displaystyle v=\frac{\pi}{2}$</td>		<td class="ntext">$\displaystyle v=\frac{\pi}{2}$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{d) }$</td>	+	<td class="ntext">d)</td>
	<td class="ntext">$\displaystyle v=\frac{\pi}{4},\displaystyle v=\frac{5\pi}{4}$</td>		<td class="ntext">$\displaystyle v=\frac{\pi}{4},\displaystyle v=\frac{5\pi}{4}$</td>
-	<td class="ntext">$\textrm{e) }$</td>	+	<td class="ntext">e)</td>
-	<td class="ntext">$\textrm{lösning saknas}$</td>	+	<td class="ntext">lösning saknas}$</td>
-	<td class="ntext">$\textrm{f) }$</td>	+	<td class="ntext">f)</td>
	<td class="ntext">$\displaystyle v=\frac{11\pi}{6}, \displaystyle v=\frac{7\pi}{6}$</td>		<td class="ntext">$\displaystyle v=\frac{11\pi}{6}, \displaystyle v=\frac{7\pi}{6}$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{g) }$</td>	+	<td class="ntext">g)</td>
	<td class="ntext">$\displaystyle v=\frac{5\pi}{6}, \displaystyle v=\frac{11\pi}{6}$</td>		<td class="ntext">$\displaystyle v=\frac{5\pi}{6}, \displaystyle v=\frac{11\pi}{6}$</td>
	<td class="ntext"></td>		<td class="ntext"></td>

Ossiang: /* Övning 4.4:2 */

2007-04-30T17:02:52Z

Övning 4.4:2

← Äldre version		Versionen från 30 april 2007 kl. 17.02
Rad 118:		Rad 118:
	</div>		</div>

-	==Övning 4.4:2==	+	==Övning 4.4:2==
	<div class="ovning">		<div class="ovning">
	Lös ekvationen		Lös ekvationen
Rad 124:		Rad 124:
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">$\sin{x}=\displaystyle \frac{\sqrt{3}}{2}$</td>		<td class="ntext">$\sin{x}=\displaystyle \frac{\sqrt{3}}{2}$</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">$\cos{x}=\displaystyle \frac{1}{2} $</td>		<td class="ntext">$\cos{x}=\displaystyle \frac{1}{2} $</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">$\sin{x}=0$</td>		<td class="ntext">$\sin{x}=0$</td>
	</tr>		</tr>
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{d) }$</td>	+	<td class="ntext">d)</td>
	<td class="ntext">$\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} $</td>		<td class="ntext">$\sin{5x}=\displaystyle \frac{1}{\sqrt{2}} $</td>
-	<td class="ntext">$\textrm{e) }$</td>	+	<td class="ntext">e)</td>
	<td class="ntext">$\sin{5x}=\displaystyle \frac{1}{2}$</td>		<td class="ntext">$\sin{5x}=\displaystyle \frac{1}{2}$</td>
-	<td class="ntext">$\textrm{f) }$</td>	+	<td class="ntext">f)</td>
	<td class="ntext">$\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}$</td>		<td class="ntext">$\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}$</td>
	</tr>		</tr>
Rad 151:		Rad 151:
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 157:		Rad 157:
	x=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$		x=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$
	</td>		</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 163:		Rad 163:
	x=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$		x=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$
	</td>		</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">		<td class="ntext">
	$x=n\pi$</td>		$x=n\pi$</td>
Rad 169:		Rad 169:
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{d) }$</td>	+	<td class="ntext">d)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 175:		Rad 175:
	x=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$		x=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$
	</td>		</td>
-	<td class="ntext">$\textrm{e) }$</td>	+	<td class="ntext">e)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 181:		Rad 181:
	x=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2}{5}n\pi } \right.$		x=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2}{5}n\pi } \right.$
	</td>		</td>
-	<td class="ntext">$\textrm{f) }$</td>	+	<td class="ntext">f)</td>
	<td class="ntext">$\left\{ \matrix{x=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2}{3}n\pi\cr		<td class="ntext">$\left\{ \matrix{x=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2}{3}n\pi\cr
	x=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2}{3}n\pi } \right.$</td>		x=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2}{3}n\pi } \right.$</td>

Ossiang: /* Övning 4.4:3 */

2007-04-30T17:01:57Z

Övning 4.4:3

← Äldre version		Versionen från 30 april 2007 kl. 17.01
Rad 232:		Rad 232:
	</div>		</div>

-	==Övning 4.4:3==	+	==Övning 4.4:3==
	<div class="ovning">		<div class="ovning">
	Lös ekvationen		Lös ekvationen
Rad 259:		Rad 259:
	<table width="100%" cellspacing="10px">		<table width="100%" cellspacing="10px">
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 266:		Rad 266:
	}\right.$		}\right.$
	</td>		</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 276:		Rad 276:
	<tr><td height="5px"/></tr>		<tr><td height="5px"/></tr>
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 283:		Rad 283:
	}\right.$		}\right.$
	</td>		</td>
-	<td class="ntext">$\textrm{d) }$</td>	+	<td class="ntext">d)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{

Ossiang: /* Övning 4.4:4 */

2007-04-30T17:00:54Z

Övning 4.4:4

← Äldre version		Versionen från 30 april 2007 kl. 17.00
Rad 324:		Rad 324:
	</div>		</div>

-	==Övning 4.4:4==	+	==Övning 4.4:4==
	<div class="ovning">		<div class="ovning">
	Bestäm de vinklar $v$ i intervallet $0^\circ \leq v \leq 360^\circ$ som uppfyller $\cos{\left(2v+10^\circ\right)}=\cos{110^\circ}$.		Bestäm de vinklar $v$ i intervallet $0^\circ \leq v \leq 360^\circ$ som uppfyller $\cos{\left(2v+10^\circ\right)}=\cos{110^\circ}$.

Ossiang: /* Övning 4.4:5 */

2007-04-30T17:00:03Z

Övning 4.4:5

← Äldre version		Versionen från 30 april 2007 kl. 17.00
Rad 343:		Rad 343:
	</div>		</div>

-	==Övning 4.4:5==	+	==Övning 4.4:5==
	<div class="ovning">		<div class="ovning">
	Lös ekvationen		Lös ekvationen
	<table width="100%" cellspacing="10px">		<table width="100%" cellspacing="10px">
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">$\sin{3x}=\sin{x}$</td>		<td class="ntext">$\sin{3x}=\sin{x}$</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">$\tan{x}=\tan{4x}$</td>		<td class="ntext">$\tan{x}=\tan{4x}$</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">$\cos{5x}=\cos(x+\pi/5)$</td>		<td class="ntext">$\cos{5x}=\cos(x+\pi/5)$</td>
	</tr>		</tr>
Rad 365:		Rad 365:
	<table width="100%" cellspacing="10px">		<table width="100%" cellspacing="10px">
	<tr align="left">		<tr align="left">
-	<td class="ntext">$\textrm{a) }$</td>	+	<td class="ntext">a)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{		$\left\{ \matrix{
Rad 372:		Rad 372:
	}\right.$		}\right.$
	</td>		</td>
-	<td class="ntext">$\textrm{b) }$</td>	+	<td class="ntext">b)</td>
	<td class="ntext">$x=\displaystyle \frac{1}{3}n\pi$</td>		<td class="ntext">$x=\displaystyle \frac{1}{3}n\pi$</td>
-	<td class="ntext">$\textrm{c) }$</td>	+	<td class="ntext">c)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{\matrix{		$\left\{\matrix{

Ossiang: /* Övning 4.4:6 */

2007-04-30T16:59:04Z

Övning 4.4:6

← Äldre version		Versionen från 30 april 2007 kl. 16.59
Rad 434:		Rad 434:
	$x=n\pi$		$x=n\pi$
	</td>		</td>
-	<td class="ntext">$b)</td>	+	<td class="ntext">b)</td>
	<td class="ntext">		<td class="ntext">
	$\left\{ \matrix{x=\displaystyle \frac{\pi}{4}+2n\pi\cr		$\left\{ \matrix{x=\displaystyle \frac{\pi}{4}+2n\pi\cr

Ossiang: /* Övning 4.4:6 */

2007-04-30T16:58:45Z

Övning 4.4:6

← Äldre version		Versionen från 30 april 2007 kl. 16.58
Rad 408:		Rad 408:
	</div>		</div>

-	==Övning 4.4:6==	+	==Övning 4.4:6==
	<div class="ovning">		<div class="ovning">
	Lös ekvationen		Lös ekvationen