Unit: 1.1.1 (b)Function

Exercise: 1.1.1. (b)[br][br]1. (a) Write the maximum and minimum values of [math] f(x) = \sin x [/math] .[br]Solution:[br]The maximum and minimum values of [math] f(x) = \sin x [/math] are +1 and -1 respectively.[br][br]1. (b) Write the maximum and minimum values of [math] f(x) = \cos x [/math] [br]Solution:[br]The maximum and minimum values of [math] f(x) = \cos x [/math] are +1 and -1 respectively.[br][br]1. (c) Write the maximum and minimum values of [math] f(x) = \tan x [/math] .[br]Solution:[br]The maximum and minimum values of [math] f(x) = \tan x [/math] are [math] + \infty [/math] and [math] - \infty [/math] respectively.[br][br]2. (a) Write the period of [math] f(x) = \sin x [/math] [br]Solution: [br]The period of [math] f(x) = \sin x [/math] is [math] 2\pi [/math] .[br][br]2. (b) Write the period of [math] f(x) = \cos x [/math] [br]Solution: [br]The period of [math] f(x) = \cos x [/math] is [math] 2\pi [/math] .[br][br]2. (c) Write the period of [math] f(x) = \tan x [/math] [br]Solution: [br]The period of [math] f(x) = \tan x [/math] is [math] \pi [/math] [br][br]3. (a) Draw the graph of [math] f(x) = \sin x ( -\pi \le x \le \pi ) [/math] [br]Solution: [math] \copyright Ambik [/math] [br]Given, [math] f(x) = \sin x ( - \pi \le x \le \pi ) [/math][br]Let us take the values of x differing 90° and corresponding values of y for [math] y = \sin x[/math]. The maximum and minimum values of [math] \sin x [/math] are 1 and [math] -1 [/math] respectively.[br][math] \begin{tabular}{|c|c|c|c|c|c|}[br]\hline [br]x & -\pi^c & -\frac{\pi^c}{2} & 0 & \frac{\pi^c}{2} & \pi^c \\[br]\hline[br]y = \sin x & 0 & - 1 & 0 & 1 & 0 \\ [br]\hline[br]\end{tabular} 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sasRxeOou5NkAsZqlpO+xm+BksuGtqx9o+c7yeaSSHES4x4UziW//7YOeZgnvG8MN/Mubxrxrzk1uNeeZ+Y7Y/0lySum31j0eXqXCpCtuevKNpd/2XjVl7hX9WYttz19+48JBZd70xe7clzY3unHnMRFm6N7L8zHhluaV4TRrdcUBN+mhW6gzXFAaLdpggrG072/cWXpOGG1qj8uGXjXnyW8bcf/l0Msek7U7i//53ZjSJIzG8+Jwxr7/WasbbkBNzSFDbHzNm8zeN+d4/TLnB6/Lf9bEm4byy16PorLR83nlkfEdtfI52ccu5eQZtSvuuSaPLEwPEDJuSOsPFM1i0wwQh8Aw/g2W5o3hNGpBltOx5qvu/fkzaD3zamJ8+aAySinQZEnNIRDt+ZMxDV/lJI0xez29IWzN3MZc2t7V3iHa2kdJ916RhlY+sSzvDNYHlZoIQdjD8DJblbuH37WtuucU6Z1mmt9wiEeC/d3cytmVcOsLlpBf2cC8nnUXM7dxoDC5nWdvC9Zb74k6cq5iLm5jcymhXuu+aNBKuLO0M1xSWmwlC2MHwM1iWu4XHWYb9uAJ3lZdZ0sAkG068to7vJNxLTqzfZhlzsAu2x+7Sgv1PfXu2trN9Z/GMdiy3FK9Jo2vyICfO1uSV4IntkjoybIMJwtq2s32n8MskaeDMwSYHd33fJ43Bf/OxhdJtCS+JvrDFmO+vjvcHX+BjYW2vjWfGa2nbNWnERs94W2lnuKaw3EwQsoOQtb0qfsGTxrYNL5o7P9KeYB/6XPMgnhtjYZnVfaljDs924DkRNwna8pP3vxR2R1Rn+87iGe1Ybilek0YitKRihk0xeAYLO5ggBJ7hZ7AsN41f0KTx6qHmC273DiRMqHioDnc+5Sys30rFHO7AeuAzfvJAv79zqTG5d1uFerB9Z/GMdiy3FK9JI4wepy4V04GOigyewYKcCULgGX4Gy3LT+AVMGri+b//jdpMGLutIFtZvpWMOry/B5Tb03e03niGRLmzfWTyjHcstxXtJA+DwU/r3Z11+COnWpeWatsNWhp/BgrumdqztNfGL9Bvh25980dz2gUOjCROTJj5f++sD5ifffmnQuGF1rxVzTz2wb9Rvq4FdP/PYi9k6sH1n8Yx2LLcU7yWNWHbGBMQsDB5CMgvDDd6aeJa7pnas7VXxC3KmgSen7dmFXWMbc9ssq3vtmMOX4lYLu8bDi7h017ewfWfxjHYstxSvSSMRTVIxw6YYPIOFHUwQAs/wM1iWm8bPedLAJRk7IbprvFWW7Tvrt3mIOTyUaC9ZufrgocbUwvadxTPasdxSvCaNRCRJxQybYvAMFnYwQQg8w89gWW4aP8dJI/afNF7H4S6M9gwWNsxTzMWeT8EdZO5zKbPSDe3U1I7lluK9pBE7jZM26DqCFbNmELK2s3hW95rasbZXxc9h0sDvUrj/NdsyXlseLox2DBZ2zFvMQbdvf7ytXewOK7bvLJ7RjuWW4r2kgWAM77iQNjjLIGaEhB01bWf5WdtrasfaXhU/Z0kDL/ezScKu8SR318Jox2Bhz7zGHN62a7Wza/xGiLuwfWfxjHYstxTfShoQ1Q1KaYOuI1Bm8IyQLHdtPKMbbK+pHWt7VfwcJQ28gtxOcnbd99pwRjsGO+8xFztbcy9XsX1n8cx4Zbml+GjSQIDitA6Xq6QNInjchcEzQsIGhrs2nrW9pnas7VXxc5A0cN09fKobrxHvuh4/q/HG6r4IMYdfD7QJ2K5xmY/tO4tntGO5pXgvacRO43Y+l/lCezdynbLUIAda9b9l2MHYzuJZbiYIa9vO9p3CV04aePbCTmZ2HV5KccdIWGb6zmBhx6LEXOyS39b1L4ZSiuo1tWO5pXgvaUCl8JY+PCgjCdpQaalBLr5mEMIOxnYWz3LX1I61vSq+YtLA68sx3myywDr2Zbc7RsIyox2DhR2LFHPh5SroPuRJcqt/Te1YbineSxoA44MHhO68aPqEKQR9+LqXR/vsMblr6dOGbrsIQrcuLTPc4KqJZ7lrasfaXhNf64nwtasPTJ7oxni7/aOHzO6d7Tc09I0BRjsGC7sWMeZC3e/7v68MmnNqasdyS/Fe0rBZ067xhKn7nw9+/jHnuqrFY41gGrrU/M+FtZ3FM7qBu6Z2rO1V8RXONPCiPXt2gfHm3ogiHTuMdgx2kWMO7+5y5zn4Ivb4QcoXNbVjuaX4ZNKASJu/u28S0DawJYJKDXIdU3Pigx2M7Sye5a6pHWt7VXzBpIFxZMeUXW++L/LwhTsoesqMdgwWZi1yzMW+S5JcGqypHcstxfcmDTQYfs+BALevLeiJYWrirRmE6JdUzFALBs9gF30As32n8IWSRmxM1b6Lh9JtwZMG+h5+z4F5rusHq2Y51tnxyvpNis9KGujUUEGlBrnO0KThqiEr19SO8Tl6WRVfIGns+FH7DMOevdfsO8u9HGIOl9/xGyT2zA9rXL7qW2pqx3JL8dlJw4oW3j/eJ6jUIMuDdc0gBD9jO4tnuWtqx9peFb/ESWPjLf6EdNfH/O8Ja/ad5V5OMRf+vCwetEwtNbVjuaV4cdKAcOGvZuEL865FapDbTs0ghB2M7Sye5a6pHWt7VfwSJo2HrvITBiam8MaSmn1nuZdbzG24yffXPZe0/WXnq5rasdxS/KCkAaFCQZFIYovUILeNmkEIOxjbWTzLXVM71vaq+CVKGuHruvHG2thSs+8s93KMOTyj5l6qQjlM9OxYB57RjvWbFD84aaCjOYJKDXIHEiPkLBzJ2M7ys9w1tWNtr4pfgqQRTjrPb3Cj3C/X7DvLvVxjDi9xDX1ov4Oy3qupHcstxVNJA4Lhx01SgkoNsk7AumYQgp+xncWz3DW1Y22vip9h0ojdUruULxzUmIMCw5a+mMPr1MN5zr0ltw/fZxUzXlluKd5LGgCHn5ynBX+2Ze/o4Rg8IGM/9mnWHHzIaesQ0paHrBlu8NXEs9w1tWNtr4mf1RPhu3/WHhN4j1tfHNfsO8u93GMu5dOa2rHcUryXNGLZEEGes3Rl4lx8jIPJvmiP4a6NZ22vqR1re1X8DM408JOjqf9KY7Fut9XsO8t9JMRc7NEDPLNWUzuWW4qfWdJA0McGC/OW3JpBqEkj758FO9m5a2kQutjauhsyaex4Zm8rYWBc5C41tWO5a45X1nYJHl+Eh/8UbH+Kexs4o53E9lgcSvEzTRowKMzEuFzlXvuLGd21jRESbUrFCO2oiWe5a2rH2l4VTySNAy/Uf4cRox2Dxdg50mIOz9jY5IF5bvcT4QySX2e0Y/0mxc88aUAmNxNDTAib+9oRV2ZGSLQjFcPlro1nba+pHWt7VfzApPHic80EYuMdMR+7NTOMsbBes+8s95EYc2uv8P0+NHEw2rF+k+KXJGnYgYCB4w4iaeJghKw96bP8Ukdaze26pnas7VXxA5LG7s3+f5x4JmNIwmBjhsWzuh+pMffAp/15Lvd9VXasYs1ol+W33/1dY1asMObrX3dpjVmzptl+7rn+9kRtSZMGePG7APYUTnrGwQgJ7iwxE+LUxLPcNbVjba+KFyYNN2Egvu+65GAiovp31ew7y30kx9wPrj3gzXNP39Pva/cIRrssv23YYMzRRxvz1rcac+BAQ71//6j++q/+qjG7drnmJMtLnjTQIXsKZ5NH7ikcIyR6nSVmQp6aeJa7pnas7VXxgqQRJgy8FqSq7WTMs7Yf6TG3/svTM07MdZLEwWiX7bdLLmnOKj7ykWbW++hHR/X9//iPiVmwvatI0gDtkMTBCAnObDHbuoy21MSz3DW1Y22vis9MGmHCsO9fq2o7GfOs7Rpzxvz4K8MSB6Ndtt8OHjTmpJOaM44vf7lJIGefLZ4niyUNzMK49mfPNrDuO+NghNSkcW9HKszbnB2IkeYYbHW/ZSSNrWv9OLYJo7rtmjQi0Zi3aZYxG8ZHzhkHM9eJbL/33iZZ4PuNN7/ZmG3buKQB8vAjfVqwD49rf/hy3H6eeWRfi9O2ASFtech61rZLbWD4GSzsrKkda3tNfN8T4Ru/9dIkdhHD3//8AS9Ga9oOvzP8DFZj7lkvDsI42XDbfm9/OJcw41Xqt8N/+qejxPHK+98/skmKL3qmYXN+eO2v64yDyb76X5+eadh4E60TZxrhf5C4FBEumAyYpSae5a45XlnblwIfxkvqt4cY7US2b9lizJve1Jxt/OIvGrNlyyhxSGK2StKAgTmJgxESHCIxI6rVxLPcNbVjba+K70ga4QQwj682Z2Oe1V1jrj2JhHET+0cDKEY7kd/+5E+a7zT+/u+bxPEHfyCeJ6slDQjVlzgYIdkBVBsvCgQYGyw1tWNtr4qPJI1w4KeuUVe1nfxHibVdYy4YhONqGD/ud2AWwWiX7bfrrmsShb176rzzRvWXr7jCmpG1nm3S2L7dmJtuMubCC4057bSRAX0dSiUORkiQ93H3KVQTz3LX1I61vSo+SBrhgE8lDI05vSTaNaeEcRQmDma8TsbLyScbs2qVMTfcYAzmYnd5/nljjj++eU5j375mD57NeMtbzOtvfKMxTz3lHp0sc0nDTRIw+JhjmkyGb+bxyZy4uxIHI2Qud0qdiTNSByX2MXgGC5NqasfaXhXvJI1woPclDOhe1XaSn7VdYy4xGRhjtj/Wfdcdo93Eb3beteu3vc2YCy5oksh73tPMyeET4V/9arP9938/bbyzV5Y0du70zyTCJGGNtWtBEMcSByOkDmD9r8+J8/ziOGlsff/13u3hOQlDY05jri/Qtj8STxzMXNeZNOw8bNf4xx5J5F//1TsTmeD7jB/vTyeN7dvN/i9+cXq5yZLnrgVJA/aEieNbNzyc2Y34YVIxwlZq4lluJgihA8PPYFluGn/ppWbrm99l7nj3pknSyE0YNDepO8vP+k1jDh7oX2IPhjLaTfyWOy/b48aXs/b/8z97SaSvB37S6LvcZMly1wMGgZs4vnTert4HAFMdnIiZOiixryae5WaCEJIw/AyW5WbxozOMt906SRqShMFy18azftOYgwfzljBx3PyJJ/OAkaMmfsudl7uOcy9n/fSnEaZmk580jjrK/06iq/Hc7ZdeakYPS+GUX/BZf97t5o6zfmJu+W+Pjta7P3y1CG+5hnBbLNY18Sz3FnwhJtA8PJbhZ7A1dR8ljN9ba+5A0vi9tebp//lvYg0Xte+z0F1jTjbP7f7wVaP5zc516/77HeJ48/yWOy/nHocvzn/nd4x573uNufnmSRLxk0ZuYwWOW/+WDzaDFwP4bbea3W9cOduEVqAPo5sBlGch/Da6JDWONcTb0//pvQtht8bY+KabBR1nu9/wX7x5bt1//vB8xt3739+RND7wAWPwLTtul/2lX+KNv+wyc+Dii4257LJBn/ve86XmMgGuL797kxmdcQjaYrhhc008y/00zjQEWoXHMvwMtobuozOMcYyNzjCQMN75zkH6LVrfXb+ztmvMDZvncMZxM66qjGNw3Xl3imJv4jc2cR53nDGnnGLMWWc132P/7d9O7cA7q8aLf6Zht9r1xo3m5c98xpj3vc+YE06QJxHy2jiukbrfceS85NCajvXkWp+7UVCuiWe59fpynqNbt9XikhQGHxLugIX1W008y60xNyBgxpA7b/jB5MYLzHPhcxyplid+kyYNXH465xwzerhv/XpjDh9O0Uz2pZNGOPFu3GjMv/yLMfiVp5wkEuIntHkFG4Rh4sj9ZayJmHl0raNq4lluq12rU5kbGH4GC/NK4VsJAz+cM77lVpNGZqA4h2nMOWIIi9Au/HI8N3FMxktf0sCcfc45xqxebQySxHiZ4O2GnrUsaYSNbd5szNVXN0nk13+9fSZCTgBuEIaJ47mMu3GlYoTdq4lnuV3twn7l1Bl+BgvbSuCjCQPkmjRywiN6jMZcVJasjVa7IYljMl7CpOEmCfzD33EmMcFnWWoMlzRCEhiGJGIvZ5ETgBXS0oSJo+92SKkYlseua+JZ7lA726fcNcPPYGHfUuM7EwbINRCjxVIAABxPSURBVGnkhkjrOI25liTZG1ztpIljMl7Gl5smZxIdSSI0aoIPd3TUZ5s0IiRSg9wmXCHtdkniYLjBVxPPcse0sxrmrBl+BrvUuj9zv/9EbusfD00aOeERPUZjLipL1sZQO0niKD3eFi5pwAMbbuoZ+GM3lRYzjA6Gn8HCjgcffDA0R1Rn+BksjFwqPBKE+8uRrYQBck0aojhxDw4nPndfTpnxO4OFbbXxMe1yE0dp2xcyacDJm7/ZPwGUFjMcGAw/g4UdB//jP4w59dTQpOw6w89gYeBS4HP/0dCkkR0io58KdWMsNvEJWqP8vhQxU8p28HRpl5M4Svd9YZMGhE5em16iyadUILGBcOiaa4z54Afj5u7ZY8yZZxpz7LHGnH66MVu3to5j+BksDJkZfs2aUR9HD4r+xm3mjr/aMTrT2HJfq7vTDXqmMdWir3TttV6MeRNfRoyFzTN+Z7Cwozbe0y4Qpi9xlLbdSxogDz/S34+dJR5Chu2F9dRv8da0HXYy/Az20KFD5vW/+Avz+q23mpdeesnT8MCBA+bwJZeY1x59dBSar191lTFnnGFeffVV7ziGn8Gyuln8qHPHHmvW/5/Hm0tSSBi/cZvBJakwhtz66DUgK1aMHux0t+eW56HvubaGx0lsR4zh1ns3xux4zY0xhn+WWLQl6XvIPQu81S7WNrY98+g+77fpv3P5K5M4Lm27lzSCBDeqwmBmYfCp7OvaFJ5xbLyl2ctwo4WaeJbb/PIvd95iZ66/fiof7rDAGUewMPwMFmbMCj86w/jQ9DLm9uP+a9DLSPUIPtOIqJHeFMSYN14zYixsnPE7g4UdtfGhFrF6eMZx3yebo0rbvhhJAw+ivOMdzeQW3ouMujEmvCsGD8aUFjN0NMM/wWb0PeQ13/ueef2P/7i1ObrhtdeMWbmytWvC39rTv4HBovVZ4B+7zjTv9Bknjd1PmOY5oj7zj8SkMTDGDH5v2lm8pOFsNx0x5h6CMuN3BstyD8YP0D2WOEr3fa6TxiSofvu3mycYf+EXJpvMn/+5MXguxFnCM47vf/6As1deLO2MqIWZffewn/qUOXz55d6mzsp3v9s8WxMcwPSdwcIMFv+dTx1sLknhBYQfMtPX64//wQi66lePxKQxMMbMlVd62nUmjY4Y88Ck39mYqYIforsx5sXnpmfPiO87LzpkXn8tVDO/Lu37/CSN2BmEO8j37zfmzW+eKvGudxlzoJ0UdvxoKug3LjxkHvjMFCItScUM28/Gz6jvE/53vtO8snbtpJosBAPfHpttuwU4awaLZhj82ivM6Nrv6NZavB0ZZxh2cePJbgvXR2LSgAaZ42siF17o+LD/WobOpNERY5O2xgXG7wwW9NXwY90P2wfxOua1UKsDL/jzHOJ9aOKQ9n1+kkaoSljHfysnnTTd+mu/Ni0HJXsKh6QBMe21v+Cw3qpUzLBBFj9pT9D30asC3vIWMwnCSSORwrp1zW2TkV2M7QwWpgzF3/WxZiBZv+O1096iScOTw6sMiDEP33XbaCLGQvxQv6MdBlsVP9YdNw+MlsS81hww/WsTh433oYlDqt1cJw3vP5cbbzTm7LOnir3hDdNypITE4Yp510XyTCwVMzSDwXtYSd9vuWV0V8uOHTtCc/z6rl3G4N1hHYvH33FM12YGizaH4EdnFuPvL+D3/Tsj32Fo0uhymTEDYixszBuv2NkTYyF+iN9tGwwWbVTDj3XfBa2w9MxrzUHTv6/s9ec5jINXD03355SkfV+cpHHRRcbgNyLscvTRzaSHl3J1LM9uerG5tu3cQSM5hZOKGZrB4D2spO9/8zcGd0c9/vjjoTnT+r59xmza1NTxZZyr6/goj3+KzCoxWBBI8BggbsJAeftTexs7cVfY7bc3Zawjd4m1OnSkXp4aEGOhdl7SyIixEC/x+yyxaIvhpvBj3bfjp7axZMxrzYHTv7t/trc1Bg6+NN3fV5L2fXGSxoknGnMP3l09XjA54ovxz3/ebmmtIYY9hXMnllcPtg6NbpCKGTbC4D2spO+4y+y558wDDzwQmjOt48E+93uU88+f7huXPP7W3vQGBouWc/GHX24njJf3OHibKNBXJAw87Ne3HKlJ48QTzet33z1VJzW+xjE2PbgpeUkjI8ZCfK7fQxzqDLYqfjy2H3vssaZbKd1jHR/3PTYWchOHVLvFSRodgqU2WzFwCucmDZRzBLX4FEdqH4NnsLDJG8ApIzv2MfwMFubk4FODJAff0e0j+t1TeBCUWZZ7zKW0oWKOHK+WG/8Mh/Pc6DJtyvDM8eY24SUNkIef0k8buvwIQrcuLbu24xQO17rdz87n9ibbd/FSbhzP4BksuGepnbTvrO19+B3PtH0J/1o7+/D2uNhanwhvzwExnWLblnPMxfrrbmNiDu0w2rncu3f+3JvjMN8988i+ydhwbbZlF2+3pdZe0nCziS0DzCwMHkIyS8gdy8R7269dmlCG+MmOzAKDZ7Awb9baZXZ5dBhrewq/56n2f1PhF38pfG8/jtTLUwP+4wy1XK4xF/YzVqdijhyvITe+tw3POLY9FLO62Rbiu49s9hxRScOKkSuoVEzbvl0zeAYL/uU4gPGiQdd3d34kfqcIpZ0mDRu+4vVyjLlcEaiYI8drFzeeUXPHi329UtinLnx4nK0fkUkDnb/nkn5BpWJaUe2awTNY8C+3AYzXwrgD4N//rvsWako7TRo2fMXr5RZzEgGomCPHa4r7x1/xx03sYecUPqbBEZs0IMYP/8kX9PurfYmkYvrovC90Q4yts9zLaQDjKW83YeDXG1MLpZ0mjZS0yX3LKeaSHY3spGJuCZMGTH3yDn/84AzdffRAavsRnTRigroPAUrFDGOJwTNY2LFcBrCbLFBO/hbG2AGUdpo0wjDOri+XmMvusHMgFXPkeM3hfn6Dnzgwlux3gTl4p6vmiE8aEKNLUKmYrrAoM3gGC+5FH8CxmxbwlH/OQmmnSSNH4ugxix5z0U5lbqRijhyvudzhiw6ROHBLbi7eSqFJY6xE7CHAbRtftDoNWkud4ZIwWLSzyAMYPzgTnmHkPFdj9aO006RhZRSvFznmqJgh/0Fkx6vE9tgbFDZ9R/Z8jiYNZ2iEt6qN7nG+3zlAWJQ4M2yawaKtRR3AuP4K3d2kYU+jQ4266pR2mjS6ZO3dvqgxh45RMTMDPKPdENtxI4kdYxhvfd8Tus7XpOGqMS4/8OlGUDt5PfQ5/4ujCCS6aYgzbUMMFm0wQQg8wz8Ue+8nfN2/9w/ldTeaNGwIiteLGHO2k0NjdlZ4Rruhtts7q+w8h7dE5/yD5iUNkIcf6dOCs8RDyLA9SZ2x/Uc37zdf++sD3tOVfU+Qh7Yx/AwWdtTUTmr77uf9p1ih+4bb9g/2vZTf9Zs+Ed6eA1x9UuVFirmwH0zMoC0Wz2jHcG/+7r7WPIfL8qE+bt1LGjZrumsczCwMHkIyC8MN3mcea78ld/sj+RYx/AwWFtbUTmL7cw9PT5Pt6fK2DfW+S9Izjfz4Do9clJgL7UZdErNLgWe0Y23Ha3ns2LPrn9wa62WzTZNGtzajQIrdxZN7uYpxJoNFl5ggBJ7hz8U+dFU7YeD0OBff5ToKr5enumTt3b4IMdfVCSpmyPECmxjtZmE7vs+1l4dt4sAT5O7zHFY7TRpWicjadUb4ICCE7bujx8VHmk9uYrBomAlC4Bn+PuxLO9rJwk3EffikcKTteqbRp273/nmOuW6rmz1VY44cr7O0PXwQED+fHS6aNEJFnHrojNillCe/5QCCYogPdierDBYNz+sAhl72Pxm7Di/5sX2n8HqmkYzL1M55jbmUzXYfFTPsPyrkeJ217XieA68bwZkHfoIgXDRphIo49ZgzYperuu46iOGd5pNFBouG520Ax3TrOltj+07hNWkk4zK1c95iLmVruI+KmWWWNKANLhNjzMYWTRoxVcbbUoEUu1z1TPBMRwqfoB3tYrBoYJ4G8Na17bOLx7/arQDbdwqvSaPbMT175inmekxt7aZiZhkmjZZAzgZNGo4YYbEvkHZubE+G37l0mqH78CGfW2ewaGceBjC+83EfIrKXo/CdRmph+07hNWmkXJPcNw8xlzQwsZOKGU0avrI1xawZhFAhp++4u+D+y9vJA7es5eB9tac1BotWamoH25+4ra0J7paK3Y0x7XVTYvtO4TVphO7IrteOuWxDIwdSMZM5V0RoJ5sY7UrbrmcaE7e1CxJn7H6iPUniScvwS942S3yLhDvWAhOEaG8oP+62sE+Y2jMLrPGLe7nLUG7bPoXXpGFlFK9rxRwMpXw+B3hGu9J995IGyMMP87Qh2mLwEDK0R1JnuIfa/sPrX548RW6fKL/zfx00z25KP2UZ9ou1vbR225980Xzzw81vsNt+I3k8fN3L5oU97bgK++vW2b4zeH0iXOYr12+lY87lZnyOdmrjGe1K2+4ljdi/FhCUWRg8hGQWhhu8Q/F4Y+59n2z/x41b2Pqu59v+DuW2+FLa4dXK4eU5JAt8t/PKXmuNbM32ncLrmYbMWc7RpWLOoZwUKZ8TY90awPIz2rHcUrwmDev1yFoqZtjEUw+0X/GNSzW4tv/ynvBov85yM0EIS/r4kRhjT3Sjf0//YJ/fGWGtj7uvOQqvSaNP3s79Sx1zncQZ8ZrCYh8VMzPAM9qVtl2TRiKaZuWM2ANto+TxOWP2bo0bwHIzQZgaRPghpNgdUeiP/VU91vaqeE0a8YDM2LpUMZdBXX3SZ2OW0Y7lluI1aSQiUipm2FSIx6SKyTX84Dd7Z/mMB+xgghB413bc8RS+XsDtw9P3+D13sf6evFpVvCaNPCdFjpplzEWaT26qGjPBeEka2rGT0a503zVpdDgRm5fKGbGH3ewkjIcG8fwHy80Eoe07zioeubad5Kyt6EdsYW2vitekEXNp1rZZxFwWUeSgqjEzg7mC0a503zVpRALQblpqZ+D21PDNknZCxpfJ319tDN53lfPDKNZmux4ShOCBTUgUsdtmYRsuTSGppZal1i3FjX0e/z33GLNyZR9kul+TxlQLYWlIzLkUnt/cHRllBovma+MZ7UrbrkkjEZClnIEvlTd/008g4aSNO5TwquKfPmgMju9bcoIQT2xve8gYPIiIF5TZhIV1yA/u3LuhSunWpYHHf+qpxqxY0XVoe7smjbYmmVtyYi7VlOe31IGRfQwWzdXGM9qVtl2TRiQA7abSzgAv3jCJn2EMJ213QrfltVeY0W/7YkLHl+1IALikhMRy2+ofj8o4K8DZA753wFPaeOcTbge2bXStwf/Ydd1f1FuNYusaurl2tPg1abjydJZbunUeGd/BTHxokeFnsCz3LPCMdqX7rkkjHv+jraWd4ZoCbtyWiwTw2BeM+fbH+yd6NwF86bxdvYnBPR5fxuP7FHxZj2dJmL4z2FkMwBa/Jg03tDrLLd06j4zvYCY+tMjwM1iWexZ4RrvSffeSBgzXz/xqcPcd95tvfn6d+drlm8zNlz1lbvzwTw2Sg/TzlQufM1/9+BZzyyc3mzVXrzd3r1m7kH6PT13NnWM2jkfHjJOG3ZZab1m1anQ56+lVqxZSk1TfdN/8ju1F8o2XNGKDsHQWc22AkMxS03bYzfBLsfi+AWcmuDyFz5r/9yODu5te2NJsx/cgOS8LtHpL+S2O7bcIj2QQ+7jGoKxnGqEi0TrjczRYc7yyttfGM9qVtl2TRnT4NBtLO8M1heVmghB2MPwMluWO4jVpuKHVWWb9pjHXKW3vDkY71m9SvCaNhDulYoZNMXgGCzuYIASe4WewLHcUr0kDsvQurN805nol7jyA0Y71mxSvSaPTjdzEiWalznBNYbBohwnC2razfffw+/Y1l6ewzln0ltsclaLHaMxFZcnayGjnxXsWm3+QFK9Jw9fPq0nF9MCaNEI5susz1d39ziPHAk0aOSpFj2EmPjTI+J3BstyzwDPale67Jo1o+DcbSzvDNYXlZoKQHQSs7VXxmjTcMBSVNeZEcnkHM9qVHi+aNDzX+ZXSznDZWW4mCGEHw89gWW4ar0nDDUNRWWNOJJd3MKNd6fGmScNznV8p7QyXneVmghB2MPwMluWm8Zo03DAUlTXmRHJ5BzPalR5vmjQ81/mV0s5w2VluJghhB8PPYFluGq9Jww1DUVljTiSXdzCjXenx5iUNkIef0r8/6/JDSLcuLde0HbYy/AwW3DW1Y22vidffCG/PAbnjTmOujnalx4uXNLzUN64gYJiFwTPZFzYz3LXxrO01tWNtr4rXM43Bw11jbrB01C3ypceLJo2En0s7wzWF5dYB7KopKGvSEIjlH6ox5+shqTHasXOFFK9JI+FZqZhhUwyewcIOJgiBZ/gZLMtN4zVpQMJBi8bcINlGIEa70uNNk0bCz6Wd4ZrCcjNBCDsYfgbLctN4TRpuGIrKGnMiubyDGe1KjzdNGp7r/EppZ7jsLDcThLCD4WewLDeN16ThhqGorDEnkss7mNGu9HjTpOG5zq+UdobLznIzQQg7GH4Gy3LTeE0abhiKyhpzIrm8gxntSo83TRqe6/xKaWe47Cw3E4Swg+FnsCw3jdek4YahqKwxJ5LLO5jRrvR406Thuc6vlHaGy85yM0EIOxh+Bsty03hNGm4YisoacyK5vIMZ7UqPN00anuv8SmlnuOwsNxOEsIPhZ7AsN43XpOGGoaisMSeSyzuY0a70ePOSBsjDT+mnDV1+COnWpeWatsNWhp/BgrumdqztNfH6RHh7DsgddxpzdbQrPV68pOGlvnEFAcMsDJ7JvrCZ4a6NZ22vqR1re1W8nmkMHu4ac4Olo56rKj1eNGkk/FzaGa4pLLcOYFdNQVmThkAs/1CNOV8PSY3Rjp0rpHhNGgnPSsUMm2LwDBZ2MEEIPMPPYFluGq9JAxIOWjTmBsk2AjHalR5vmjQSfi7tDNcUlpsJQtjB8DNYlpvGa9Jww1BU1pgTyeUdzGhXerxp0vBc51dKO8NlZ7mZIIQdDD+DZblpvCYNNwxFZY05kVzewYx2pcebJg3PdX6ltDNcdpabCULYwfAzWJabxmvScMNQVNaYE8nlHcxoV3q8adLwXOdXSjvDZWe5mSCEHQw/g2W5abwmDTcMRWWNOZFc3sGMdqXHmyYNz3V+pbQzXHaWmwlC2MHwM1iWm8Zr0nDDUFTWmBPJ5R3MaFd6vGnS8FznV0o7w2VnuZkghB0MP4NluWm8Jg03DEVljTmRXN7BjHalx5uXNEAefko/bejyQ0i3Li3XtB22MvwMFtw1tWNtr4nXJ8Lbc0DuuNOYq6Nd6fHiJQ0v9Y0rCBhmYfBM9oXNDHdtPGt7Te1Y26vi9Uxj8HDXmBssHfVcVenxokkj4efSznBNYbl1ALtqCsqaNARi+YdqzPl6SGqMduxcIcVr0kh4Vipm2BSDZ7CwgwlC4Bl+Bsty03hNGpBw0KIxN0i2EYjRrvR406SR8HNpZ7imsNxMEMIOhp/Bstw0XpOGG4aissacSC7vYEa70uNNk4bnOr9S2hkuO8vNBCHsYPgZLMtN4zVpuGEoKmvMieTyDma0Kz3eNGl4rvMrpZ3hsrPcTBDCDoafwbLcNF6ThhuGorLGnEgu72BGu9LjTZOG5zq/UtoZLjvLzQQh7GD4GSzLTeM1abhhKCprzInk8g5mtCs93jRpeK7zK6Wd4bKz3EwQwg6Gn8Gy3DRek4YbhqKyxpxILu9gRrvS402Thuc6v1LaGS47y80EIexg+Bksy03jNWm4YSgqa8yJ5PIOZrQrPd68pAHy8FP6aUOXH0K6dWm5pu2wleFnsOCuqR1re028PhHengNyx53GXB3tSo8XL2l4qW9cQcAwC4Nnsi9sZrhr41nba2rH2l4Vr2cag4e7xtxg6ajnqkqPF00aCT+XdoZrCsutA9hVU1DWpCEQyz9UY87XQ1JjtGPnCilek0bCs1Ixw6YYPIOFHUwQAs/wM1iWm8Zr0oCEgxaNuUGyjUCMdqXHmyaNhJ9LO8M1heVmghB2MPwMluWm8Zo03DAUlTXmRHJ5BzPalR5vmjQ81/mV0s5w2VluJghhB8PPYFluEf6004xZsSLvc/zxrns6ywvT90gPWNs15iKiZm5itGP9JsVr0kg4VSpm2BSDZ7CwgwlC4Bl+Bstye/g9e4w580xjjj3WmNNPN2brVuyeLhdckJcwkFjOPXeKS5Tmpu8JG7t2sbZrzHUp27+d0Y71mxSvSSPhT6mYYVMMnsHCDiYIgWf4GSzL7eEvu8yYdeuwyZirrzbmjDOasv170035SWP1aotKruem70kr4ztZ2zXm4rrmbGW0Y/0mxWvSSHhUKmbYFINnsLCDCULgGX4Gy3J7+OuvR7VZDh9uzjhsHevt24055pi8xLF+vYvsLM9N3zst7N7B2q4x161t3x5GO9ZvUrwmjYQ3pWKGTTF4Bgs7mCAEnuFnsCx3J/6114xZuRK7/eXkk/uTxgknGIOkk7HMZd8z7MYhrO0ac5lCRw5jtGP9JsV7SQOG60c1WJQYiIy90abQ/kcffdT8fM0ac+iznzVPPPGEF+Pb3vve3qTx/B/+oYcJ29e6jpkjKQa8pBEbhNIsFLbB4OEIZmG4wVsTz3LX1I61PRvfdedTLGiuvDK21Zic7zUyv8+oHTMsf7bucSX17LZDl5zNzHhl/SbFa9JIeFQqZtgUg2ewsIMJQuAZfgbLckfx+DJ82zbsai8532ts3NjGdWyZu7532BnbzNquMRdTNW8box3rNylek0bCp1Ixw6YYPIOFHUwQAs/wM1iWu4XftcuYzZuxuXtJPa8h+D4DBHPV9+4eR/ewtmvMRWXN2shox/pNitekkXCpVMywKQbPYGEHE4TAM/wMluX28Pv2GbNpEzYZg7ufVq1qyuHfCy/s/l7jnHPCo5P1uel70sr4TtZ2jbm4rjlbGe1Yv0nxmjQSHpWKGTbF4Bks7GCCEHiGn8Gy3B4eD/a533ucfz52t5cbbvCPczF4vkOwzE3fBTbbQ1nbNeaskvI1ox3rNylek0bCv1Ixw6YYPIOFHUwQAs/wM1iWexB+587upJH5fAZ4sSxc38d2z8J2jTlHTGGR0a50zGnSSDi3tDNcU1huJghhB8PPYFnuwfjY9xqZ75uapd9qasdya8y5kSArM9qxfpPiNWkkfCsVM2yKwTNY2MEEIfAMP4NluQfjY++hynzfFDjtspB9HxvP2q4xZ6NAvma0Y/0mxWvSSPhXKmbYFINnsLCDCULgGX4Gy3IPxsee1xA8nwFeLAvZ9xnZrjE3FnLAitGudMx5SQPk4af078+6/BDSrUvLNW2HrQw/gwV3Te1Y22vg9+Iuq+A9VPsefFAcfzVsd8cFw89gNeaeFceK6zdmvLJ+k+K9pBFLkOgYszB4JvvCZoa7Np61vaZ2rO3V8O57qI47Lvt9U+74qGb72AiGn8GCXmPOjQRZmdGO9ZsUr0kj4VupmGFTDJ7Bwg4mCIFn+Bksy03h3ec1TjkFTYmXhe076XMIpTEnDpcJgNGudMxp0pi4rV0o7QzXApabCULYwfAzWJabwrvfa5x1luuO7PLC9p30OQTSmMsOk9aBjHalY06TRst90w2lnTFl5iZttMMEIfBM3xksy03h8R6qo45qntnAWceAZWH7TvocUmnMDQiYMYTRrnTMuUnj/wOHDBBITDmUFAAAAABJRU5ErkJggg==[/img][br][br]3. (b) Draw the graph of [math] f(x) = \cos x ( 0 \le x \le 2\pi ) [/math] [br]Solution:[br]Given, [math] f(x) = \cos x (0 \le x \le 2\pi ) [/math][br]Let us take the values of x differing 90° and corresponding values of y for [math] y = \cos x. [/math] The maximum and minimum values of [math] \cos x [/math] are 1 and [math] -1 [/math] respectively.[br]Now, [math] \begin{tabular}{|c|c|c|c|c|c|}[br]\hline [br]x & 0 & \frac{\pi^c}{2} & \pi^c & \frac{3\pi^c}{2}& 2\pi^c \\[br]\hline[br]y = \cos x & 1 & 0 & -1 & 0 & 1 \\ [br]\hline[br]\end{tabular} 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[/img][br]3. (c) Draw the graph of [math] f(x) = \tan x ( 0 \le x \le \pi ) [/math] [br]Solution: [br]Given, [math] f(x) = \tan x \ ( 0\le x \le \pi ) [/math] [br]Now, [math] \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}[br]\hline [br]x & 0 & \frac{\pi^c}{6} & \frac{\pi^c}{4} & \frac{\pi^c}{3}& \frac{\pi^c}{2} & \frac{2\pi^c}{3} & \frac{3\pi^c}{4} & \frac{5\pi^c}{6}& \pi^c \\[br]\hline[br]y = \tan x & 0 & 0.58 & 1 & 1.73 & \text{Undefined} & - 1.73 & - 1 & - 0.58 & 0\\[br]\hline[br]\end{tabular} [/math][br][img]data:image/png;base64,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[/img][br][br]3. (d) Draw the graph of [math] f(x) = 2\sin x \left( -\frac{\pi}{2} < x < \frac{\pi}{2} \right) [/math] [br]Solution: [br]Given, [math] \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}[br]\hline [br]x & \frac{-\pi^c}{2} & \frac{-\pi^c}{3} & \frac{-\pi^c}{4}& \frac{\pi^c}{6} & 0 & \frac{\pi^c}{6} & \frac{\pi^c}{4} & \frac{\pi^c}{3} & \frac{\pi^c}{2} \\[br]\hline[br]y = 2 \sin x & - 2 & - 1.73 & -1.41& - 1 & 0 &1&1.41&1.73&2 \\ [br]\hline[br]\end{tabular} [/math][br] 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[/img][br][br]4. Study the topic 'sound' in physics of your science book and find the nature of longitudinal wave. Relate this concept with trigonometric function.[br]Solution:[br]The nature of longitudinal wave is like the graph of sine function.

Information: Unit: 1.1.1 (b)Function