Sommarmatte 1
(Skillnad mellan versioner)
Versionen från 16 juli 2007 kl. 09.26
Svar 1.1:1
Svar 1.1:2
Svar 1.1:3
| a) |
naturliga talen, heltalen, rationella talen |
b) |
heltalen, rationella talen |
c) |
naturliga talen, heltalen, rationella talen |
| d) |
heltalen, rationella talen |
e) |
heltalen, rationella talen |
f) |
naturliga talen, heltalen, rationella talen |
| g) |
rationella talen |
h) |
naturliga talen, heltalen, rationella talen |
i) |
irrationella talen |
| j) |
naturliga talen, heltalen, rationella talen |
k) |
irrationella talen |
l) |
irrationella talen |
Svar 1.1:4
| a) |
\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3} |
| b) |
\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5} |
| c) |
\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3} |
Svar 1.1:5
| a) |
1{,}167 |
b) |
2{,}250 |
c) |
0{,}286 |
d) |
1{,}414 |
Svar 1.1:6
| a) |
Talet är rationellt och lika med \,314/100 = 157/50\,. |
| b) |
Talet är rationellt och är lika med \,31413/9999 = 10471/3333\,. |
| c) |
Talet är rationellt och lika med \,1999/9990\,. |
| d) |
Talet är irrationellt. |
Svar 1.2:1
| a) |
\displaystyle \frac{93}{28} |
b) |
\displaystyle \frac{3}{35} |
c) |
\displaystyle -\frac{7}{30} |
| d) |
\displaystyle \frac{47}{60} |
e) |
\displaystyle \frac{47}{84} |
Svar 1.2:2
| a) |
\displaystyle {30} |
b) |
\displaystyle {8} |
| c) |
\displaystyle {84} |
d) |
\displaystyle {225} |
Svar 1.2:3
| a) |
\displaystyle \frac{19}{100} |
b) |
\displaystyle \frac{1}{240} |
Svar 1.2:4
| a) |
\displaystyle \frac{6}{7} |
b) |
\displaystyle \frac{16}{21} |
c) |
\displaystyle \frac{1}{6} |
Svar 1.2:5
| a) |
\displaystyle \frac{105}{4} |
b) |
-5 |
c) |
\displaystyle \frac{8}{55} |
Svar 1.2:6
| \displaystyle \frac{152}{35} |
Svar 1.3:1
| a) |
72 |
b) |
3 |
c) |
-125 |
d) |
\displaystyle \frac{27}{8} |
Svar 1.3:2
Svar 1.3:3
| a) |
3^{-1} |
b) |
3^5 |
c) |
3^4 |
d) |
3^{-3} |
e) |
3^{-3} |
Svar 1.3:4
| a) |
4 |
b) |
3 |
c) |
625 |
| d) |
16 |
e) |
\displaystyle \frac{1}{3750} |
Svar 1.3:5
| a) |
2 |
b) |
\displaystyle \frac{1}{2} |
c) |
27 |
| d) |
2209 |
e) |
9 |
f) |
\displaystyle \frac{25}{3} |
Svar 1.3:6
| a) |
256^{1/3}>200^{1/3} |
b) |
0{,}4^{-3}>0{,}5^{-3} |
c) |
0{,}2^{5}>0{,}2^{7} |
| d) |
\bigl(5^{1/3}\bigr)^{4}>400^{1/3} |
e) |
125^{1/2}>625^{1/3} |
f) |
3^{40}>2^{56} |
Svar 2.1:1
| a) |
3x^2-3x |
b) |
xy+x^2y-x^3y |
c) |
-4x^2+x^2y^2 |
| d) |
x^3y-x^2y+x^3y^2 |
e) |
x^2-14x+49 |
f) |
16y^2+40y+25 |
| g) |
9x^6-6x^3y^2+y^4 |
h) |
9x^{10}+30x^8+25x^6 |
Svar 2.1:2
| a) |
-5x^2+20 |
b) |
10x-11 |
| c) |
54x |
d) |
81x^8-16 |
| e) |
2a^2+2b^2 |
Svar 2.1:3
| a) |
(x+6)(x-6) |
b) |
5(x+2)(x-2) |
c) |
(x+3)^2 |
| d) |
(x-5)^2 |
e) |
-2x(x+3)(x-3) |
f) |
(4x+1)^2 |
Svar 2.1:4
| a) |
5\, framför \,x^2\,, \,3\, framför \,x |
| b) |
2\, framför \,x^2\,, \,1\, framför \,x |
| \textrm{c) } |
6\, framför \,x^2\,, \,2\, framför \,x |
Svar 2.1:5
| a) |
\displaystyle \frac{1}{1-x} |
b) |
-\displaystyle \frac{1}{y(y+2)} |
| c) |
3(x-2)(x-1) |
d) |
\displaystyle \frac{2(y+2)}{y^2+4} |
Svar 2.1:6
| a) |
2y |
b) |
\displaystyle\frac{-x+12}{(x-2)(x+3)} |
| c) |
\displaystyle\frac{b}{a(a-b) } |
d) |
\displaystyle\frac{a(a+b) }{4b} |
Svar 2.1:7
| a) |
\displaystyle \frac{4}{(x+3)(x+5)} |
b) |
\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)} |
c) |
\displaystyle \frac{ax(a+1-x)}{(a+1)^2} |
Svar 2.1:8
| a) |
\displaystyle \frac{x}{(x+3)(x+1)} |
b) |
\displaystyle \frac{2(x-3)}{x} |
c) |
\displaystyle \frac{x+2}{2x+3} |
Svar 2.2:1
| a) |
x=1 |
b) |
x=6 |
| c) |
x=-\displaystyle\frac{3}{2} |
d) |
x=-\displaystyle\frac{13}{3} |
Svar 2.2:2
| a) |
x=1 |
b) |
x=\displaystyle\frac{5}{3} |
| c) |
x=2 |
d) |
x=-2 |
Svar 2.2:3
| a) |
x=9 |
| b) |
x=\displaystyle\frac{7}{5} |
| c) |
x=\displaystyle\frac{4}{5} |
| d) |
x=\displaystyle\frac{1}{2} |
Svar 2.2:4
| a) |
-2x+y=3 |
| b) |
y=-\displaystyle\frac{3}{4}x+\frac{5}{4} |
|
Svar 2.2:5
| a) |
y=-3x+9 |
| b) |
y=-3x+1 |
| c) |
y=3x+5 |
| d) |
y=-\displaystyle \frac{1}{2}x+5 |
| e) |
k = \displaystyle\frac{8}{5} |
Svar 2.2:6
| a) |
\bigl(-\frac{5}{3},0\bigr) |
b) |
(0,5) |
| c) |
\bigl(0,-\frac{6}{5}\bigr) |
d) |
(12,-13) |
| e) |
\bigl(-\frac{1}{4},\frac{3}{2}\bigr) |
Svar 2.2:7
Svar 2.2:8
Svar 2.2:9
| a) |
4\, a.e. |
| b) |
5\, a.e. |
| c) |
6\, a.e. |
Svar 2.3:1
| a) |
(x-1)^2-1 |
b) |
(x+1)^2-2 |
c) |
-(x-1)^2+6 |
d) |
\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4} |
Svar 2.3:2
| a) |
\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right. |
b) |
\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right. |
c) |
saknar (reella) lösning |
| d) |
\left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right. |
e) |
\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right. |
f) |
\left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right. |
Svar 2.3:3
| a) |
\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right. |
b) |
\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. |
| c) |
\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. |
d) |
\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. |
| e) |
\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. |
f) |
\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. |
Svar 2.3:4
| a) |
ax^2-ax-2a=0\,, där \,a\ne 0\, är en konstant. |
| b) |
ax^2-2ax-2a=0\,, där \,a\ne 0\, är en konstant. |
| c) |
ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,, där \,a\ne 0\, är en konstant. |
Svar 2.3:5
| a) |
Exempelvis \ x^2+14x+49=0\,. |
| b) |
3< x<4 |
| c) |
b=-5 |
Svar 2.3:6
| a) |
0 |
b) |
-2 |
c) |
\displaystyle \frac{3}{4} |
Svar 2.3:7
| a) |
1 |
b) |
\displaystyle -\frac{7}{4} |
c) |
saknar max |
Svar 2.3:8
| Se lösningen i
webmaterialet när du loggat in till kursen. |
Svar 2.3:9
| a) |
(-1,0)\ och \ (1,0) |
b) |
(2,0)\ och \ (3,0) |
c) |
(1,0)\ och \ (3,0) |
Svar 2.3:10
| Se lösningen i webmaterialet när du loggat in till kursen |
Svar 3.1:1
| a) |
2^{1/2} |
b) |
7^{5/2} |
c) |
3^{4/3} |
d) |
3^{1/4} |
Svar 3.1:2
| a) |
3 |
b) |
3 |
c) |
ej definierad |
d) |
5^{11/6} |
| e) |
12 |
f) |
2 |
g) |
-5 |
|
|
Svar 3.1:3
| a) |
3 |
b) |
\displaystyle \frac{4\sqrt{3}}{3} |
| c) |
2\sqrt{5} |
d) |
2-\sqrt{2} |
Svar 3.1:4
| a) |
0{,}4 |
b) |
0{,}3 |
| c) |
-4\sqrt{2} |
d) |
2\sqrt{3} |
Svar 3.1:5
| a) |
\displaystyle \frac{\sqrt{3}}{3} |
b) |
\displaystyle \frac{7^{2/3}}{7} |
c) |
3-\sqrt{7} |
d) |
\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4} |
Svar 3.1:6
| a) |
6+2\sqrt{2}+3\sqrt{5}+\sqrt{10} |
b) |
-\displaystyle \frac{5+4\sqrt{3}}{23} |
| c) |
\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5} |
d) |
\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23} |
Svar 3.1:7
| a) |
\sqrt{5}-\sqrt{7} |
b) |
-\sqrt{35} |
c) |
\sqrt{17} |
Svar 3.1:8
| a) |
\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5 |
b) |
7 > \sqrt7 |
| c) |
\sqrt7 > 2{,}5 |
d) |
\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3 |
Svar 3.2:1
Svar 3.2:2
Svar 3.2:3
| \left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right. |
Svar 3.2:4
Svar 3.2:5
Svar 3.2:6
| x=\displaystyle\frac{5}{4} |
Svar 3.3:1
| a) |
x=3 |
b) |
x=-1 |
| c) |
x=-2 |
d) |
x=4 |
Svar 3.3:2
| a) |
-1 |
b) |
4 |
c) |
-3 |
d) |
0 |
| e) |
2 |
f) |
3 |
g) |
10 |
h) |
-2 |
Svar 3.3:3
| a) |
3 |
b) |
-\displaystyle \frac{1}{2} |
c) |
-3 |
| d) |
\displaystyle \frac{7}{3} |
e) |
4 |
f) |
-2 |
| g) |
1 |
h) |
\displaystyle \frac{5}{2} |
Svar 3.3:4
| a) |
1 |
b) |
0 |
c) |
-\displaystyle \frac{1}{2}\lg{3} |
Svar 3.3:5
| a) |
5 |
b) |
0 |
c) |
0 |
| d) |
0 |
e) |
-2 |
f) |
e^2 |
Svar 3.3:6
|
| a) |
1{,}262 |
| b) |
1{,}663 |
| c) |
4{,}762 |
Svar 3.4:1
| a) |
x=\ln 13 |
b) |
x=\displaystyle\frac{\ln 2 - \ln 13}{1+\ln 3} |
c) |
x=\displaystyle\frac{\ln 7 - \ln 3}{1-\ln 2} |
Svar 3.4:2
| a) |
\left\{ \eqalign{ x_1&=\sqrt2 \cr x_2&=-\sqrt2 } \right. |
b) |
x=\ln \left(\displaystyle\frac{\sqrt17}{2}-\frac{1}{2}\right) |
c) |
Saknar lösning |
Svar 3.4:3
| a) |
x=-\,\displaystyle\frac{1}{\ln{2}}\pm\sqrt{\left(\displaystyle\frac{1}{\ln{2}}\right)^2-1} |
b) |
x=\displaystyle \frac{5}{2} |
| c) |
x=1 |
Svar 4.1:1
| a) |
90^\circ\ och \ \displaystyle \frac{\pi}{2} \textrm{ rad} |
b) |
135^\circ\ och \ \displaystyle \frac{3\pi}{4} \textrm{ rad} |
| c) |
-240^\circ\ och \ \displaystyle -\frac{4\pi}{3} \textrm{ rad} |
d) |
2910^\circ\ och \ \displaystyle \frac{97\pi}{6} \textrm{ rad} |
Svar 4.1:2
| a) |
\displaystyle \frac{\pi}{4}\textrm{ rad} |
b) |
\displaystyle \frac{3\pi}{4}\textrm{ rad} |
c) |
-\displaystyle \frac{7\pi}{20}\textrm{ rad} |
d) |
\displaystyle \frac{3\pi}{2}\textrm{ rad} |
Svar 4.1:3
Svar 4.1:4
| a) |
5 \textrm{ l.e.} |
| b) |
\sqrt{61} \textrm{ l.e.} |
| c) |
(2,0) |
Svar 4.1:5
| a) |
(x-1)^2+(y-2)^2=4 |
| b) |
(x-2)^2+(y+1)^2=13 |
Svar 4.1:6
| a) |
En cirkel med radie 3 och medelpunkt i origo. |
b) |
En cirkel med radie \sqrt 3 och medelpunkt i punkten (1, 2). |
| c) |
En cirkel med radie \frac{1}{3}\sqrt 10 och medelpunkt i punkten (1/3, -7/3). |
Svar 4.1:7
| a) |
En cirkel med medelpunkt (-1, 1) och radie \sqrt 3. |
b) |
En cirkel med medelpunkt (0, -2) och radie 2. |
| c) |
En cirkel med medelpunkt (1, -3) och radie \sqrt 7. |
| d) |
Endast punkten (1, -1). |
Svar 4.1:8
|
\displaystyle \frac{10}{\pi}\textrm{ varv }\approx 3,2 \textrm{ varv} |
Svar 4.1:9
| \displaystyle \frac{32\pi}{3} \textrm{ cm}^2 \approx 33,5 \textrm{ cm}^2 |
Svar 4.1:10
Svar 4.2:1
Facit till alla delfrågor
| a) |
x=13\cdot\tan {27 ^\circ} \approx 6{,}62 |
b) |
x=25\cdot\cos {32 ^\circ} \approx 21{,}2 |
| c) |
x=\displaystyle\frac{14}{\tan {40 ^\circ}} \approx 16{,}7 |
d) |
x=\displaystyle\frac{16}{\cos {20 ^\circ}} \approx 17{,}0 |
| e) |
x=\displaystyle\frac{11}{\sin {35 ^\circ}} \approx 19{,}2 |
f) |
x=\displaystyle\frac{19}{\tan {50 ^\circ}} \approx 15{,}9 |
Svar 4.2:2
| a) |
\tan v=\displaystyle\frac{2}{5} |
b) |
\sin v=\displaystyle\frac{7}{11} |
| c) |
\cos v=\displaystyle\frac{5}{7} |
d) |
\sin v=\displaystyle\frac{3}{5} |
| e) |
v=30 ^\circ |
f) |
\sin \displaystyle\frac{v}{2}=\displaystyle\frac{1}{3} |
Svar 4.2:3
| a) |
-1 |
b) |
1 |
c) |
0 |
| d) |
0 |
e) |
\displaystyle \frac{1}{\sqrt{2}} |
f) |
\displaystyle \frac{\sqrt{3}}{2} |
Svar 4.2:4
| a) |
\displaystyle \frac{\sqrt{3}}{2} |
b) |
\displaystyle \frac{1}{2} |
c) |
-1 |
| d) |
0 |
e) |
\displaystyle \frac{1}{\sqrt{3}} |
f) |
\sqrt{3} |
Svar 4.2:5
| a) |
-\displaystyle \frac{1}{\sqrt{2}} |
b) |
1 |
c) |
\displaystyle \frac{\sqrt{3}}{2} |
d) |
-1 |
Svar 4.2:6
Svar 4.2:7
| Älvens bredd är \ \displaystyle\frac{100}{\sqrt{3}-1} m \approx 136{,}6 m. |
Svar 4.2:8
| \ell\cos \gamma=a \cos \alpha - b\cos \beta |
Svar 4.2:9
| Avståndet är \ \sqrt{205-48\sqrt{3}} \approx 11{,}0 km. |
Svar 4.3:1
| a) |
v = \displaystyle \frac{9\pi}{5} |
b) |
v = \displaystyle \frac{6\pi}{7} |
c) |
v = \displaystyle \frac{9\pi}{7} |
Svar 4.3:2
| a) |
v=\displaystyle \frac{\pi}{2} |
b) |
v=\displaystyle \frac{3\pi}{5} |
Svar 4.3:3
| a) |
-a |
b) |
a |
| c) |
\sqrt{1-a^2} |
d) |
\sqrt{1-a^2} |
| e) |
-a |
f) |
\displaystyle \frac{\sqrt{3}}{2}\sqrt{1-a^2}+\displaystyle \frac{1}{2}\cdot a |
Svar 4.3:4
| a) |
1-b^2 |
b) |
\sqrt{1-b^2} |
| c) |
2b\sqrt{1-b^2} |
d) |
2b^2-1 |
| e) |
\sqrt{1-b^2}\cdot\displaystyle \frac{1}{\sqrt{2}} + b\cdot \displaystyle \frac{1}{\sqrt{2}} |
f) |
b\cdot\displaystyle \frac{1}{2}+\sqrt{1-b^2}\cdot\displaystyle \frac{\sqrt{3}}{2} |
Svar 4.3:5
| \cos{v}=\displaystyle \frac{2\sqrt{6}}{7}\quad och \quad\tan{v}=\displaystyle \frac{5}{2\sqrt{6}}\,. |
Svar 4.3:6
| a) |
\sin{v}=-\displaystyle \frac{\sqrt{7}}{4}\quad och \quad\tan{v}=-\displaystyle \frac{\sqrt{7}}{3}\,. |
| b) |
\cos{v}=-\displaystyle \frac{\sqrt{91}}{10}\quad och \quad\tan{v}=-\displaystyle \frac{3}{\sqrt{91}}\,. |
| c) |
\sin{v}=-\displaystyle \frac{3}{\sqrt{10}}\quad och \quad\cos{v}=-\displaystyle \frac{1}{\sqrt{10}}\,. |
Svar 4.3:7
| a) |
\sin{(x+y)}=\displaystyle \frac{4\sqrt{2}+\sqrt{5}}{9} |
| b) |
\sin{(x+y)}=\displaystyle \frac{3\sqrt{21}+8}{25} |
Svar 4.3:8
| Se lösningen i webmaterialet när
du loggat in till kursen |
Svar 4.3:9
| Se lösningen i webmaterialet när
du loggat in till kursen |
Svar 4.4:1
| a) |
\displaystyle v=\frac{\pi}{6}\,, \,\displaystyle v=\frac{5\pi}{6} |
b) |
\displaystyle v=\frac{\pi}{3}\,, \,\displaystyle v=\frac{5\pi}{3} |
| c) |
\displaystyle v=\frac{\pi}{2} |
d) |
\displaystyle v=\frac{\pi}{4}\,, \,\displaystyle v=\frac{5\pi}{4} |
| e) |
lösning saknas |
f) |
\displaystyle v=\frac{11\pi}{6}\,, \,\displaystyle v=\frac{7\pi}{6} |
| g) |
\displaystyle v=\frac{5\pi}{6}\,, \,\displaystyle v=\frac{11\pi}{6} |
Svar 4.4:2
| a) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.
|
b) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.
|
c) |
x=n\pi |
| d) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr
x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.
|
e) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr
x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.
|
f) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr
x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.
|
Svar 4.4:3
| a) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{6}+2n\pi\cr
x&=\displaystyle\frac{11\pi}{6}+2n\pi
}\right.
|
b) |
\left\{\eqalign{
x&=\displaystyle\frac{\pi}{5}+2n\pi\cr
x&=\displaystyle\frac{4\pi}{5}+2n\pi
}\right.
|
| c) |
\left\{\eqalign{
x&=25^\circ + n\cdot 360^\circ\cr
x&=75^\circ + n\cdot 360^\circ
}\right.
|
d) |
\left\{\eqalign{
x&=5^\circ + n \cdot 120^\circ \cr
x&= 55^\circ + n \cdot 120^\circ
}\right.
|
Svar 4.4:4
|
v_1=50^\circ, \ \ v_2=120^\circ, \ \ v_3=230^\circ\ \ och \ \ v_4=300^\circ
|
Svar 4.4:5
| a) |
\left\{\eqalign{
x&=n\pi\cr
x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
}\right.
|
b) |
x=\displaystyle \frac{n\pi}{3} |
| c) |
\left\{\eqalign{
x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr
x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3}
}\right.
|
Svar 4.4:6
| a) |
x=n\pi
|
b) |
\left\{\eqalign{
x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
x&=\displaystyle \frac{\pi}{2}+n\pi\cr
x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.
|
| c) |
\left\{\eqalign{
x&=\displaystyle \frac{2n\pi}{3}\cr
x&=\displaystyle \pi + 2n\pi\cr
}\right.
|
Svar 4.4:7
| a) |
\left\{ \matrix{
x=\displaystyle \frac{\pi}{6}+2n\pi\cr
x=\displaystyle \frac{5\pi}{6}+2n\pi\cr
x=\displaystyle \frac{3\pi}{2}+2n\pi
}\right.
|
b) |
x=\pm \displaystyle \frac{\pi}{3} + 2n\pi |
| c) |
\left\{ \matrix{
x=\displaystyle \frac{\pi}{2}+2n\pi\cr
x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7}
}\right.
|
Svar 4.4:8
| a) |
\left\{\eqalign{
x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
x&=\displaystyle \frac{\pi}{2}+n\pi\cr
x&=\displaystyle \frac{3\pi}{4}+2n\pi
}\right.
|
b) |
x=\displaystyle \frac{\pi}{3}+n\pi |
| c) |
\left\{\eqalign{
x&=n\pi\cr
x&=\displaystyle \frac{3\pi}{4}+n\pi
}\right.
|
