Facit

Sommarmatte 1

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Svar 1.1:1

a) $-7$ b) $1$
c) $11$ d) $1$

Svar 1.1:2

a) $0$ b) $-1$
c) $-25$ d) $-19$

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

a) $2^6$ b) $2^{-2}$ c) $2^0$

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

a) Bild:Svar_o2_2_7a.gif‎ b) Bild:Svar_o2_2_7b.gif‎
c) Bild:Svar_o2_2_7c.gif‎

Svar 2.2:8

a) Bild:Svar_o2_2_8a.gif‎ b) Bild:Svar_o2_2_8b.gif‎
c) Bild:Svar_o2_2_8c.gif‎

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

$x=5$

Svar 3.2:2

$x=1$

Svar 3.2:3

$\left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right.$

Svar 3.2:4

Saknar lösning.

Svar 3.2:5

$x=1$

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

a) $x=50$ b) $x=5$ c) $x=15$

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

$x=9$ dm

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

$x= \sqrt{3}-1$

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)

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{3\pi}{4}+n\pi }\right.$

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