1.在“解直角三角形”一章我們學(xué)習(xí)到“銳角的正弦、余弦、正切都是銳角的函數(shù),統(tǒng)稱為銳角三角函數(shù)”.
小力根據(jù)學(xué)習(xí)函數(shù)的經(jīng)驗(yàn),對(duì)銳角的正弦函數(shù)進(jìn)行了探究.下面是小力的探究過(guò)程,請(qǐng)補(bǔ)充完成:
(1)函數(shù)的定義是:“一般地,在一個(gè)變化的過(guò)程中,有兩個(gè)變量x和y,對(duì)于變量x的每一個(gè)值,變量y都有唯一確定的值和它對(duì)應(yīng),我們就把x稱為自變量,y稱為因變量,y是x的函數(shù)”.由函數(shù)定義可知,銳角的正弦函數(shù)的自變量是銳角的角度,因變量是正弦值,自變量的取值范圍是大于0°且小于90°.
(2)利用描點(diǎn)法畫函數(shù)的圖象.小力先上網(wǎng)查到了整銳角的正弦值,如下:
sin1°=0.01745240643728351 sin2°=0.03489949670250097 sin3°=0.05233595624294383
sin4°=0.0697564737441253 sin5°=0.08715574274765816 sin6°=0.10452846326765346
sin7°=0.12186934340514747 sin8°=0.13917310096006544 sin9°=0.15643446504023087
sin10°=0.17364817766693033 sin11°=0.1908089953765448 sin12°=0.20791169081775931
sin13°=0.22495105434386497 sin14°=0.24192189559966773 sin15°=0.25881904510252074
sin16°=0.27563735581699916 sin17°=0.2923717047227367 sin18°=0.3090169943749474
sin19°=0.3255681544571567 sin20°=0.3420201433256687 sin21°=0.35836794954530027
sin22°=0.374606593415912 sin23°=0.3907311284892737 sin24°=0.40673664307580015
sin25°=0.42261826174069944 sin26°=0.4383711467890774 sin27°=0.45399049973954675
sin28°=0.4694715627858908 sin29°=0.48480962024633706 sin30°=0.5000000000000000
sin31°=0.5150380749100542 sin32°=0.5299192642332049 sin33°=0.544639035015027
sin34°=0.5591929034707468 sin35°=0.573576436351046 sin36°=0.5877852522924731
sin37°=0.6018150231520483 sin38°=0.6156614753256583 sin39°=0.6293203910498375
sin40°=0.6427876096865392 sin41°=0.6560590289905073 sin42°=0.6691306063588582
sin43°=0.6819983600624985 sin44°=0.6946583704589972 sin45°=0.7071067811865475
sin46°=0.7193398003386511 sin47°=0.7313537016191705 sin48°=0.7431448254773941
sin49°=0.7547095802227719 sin50°=0.766044443118978 sin51°=0.7771459614569708
sin52°=0.7880107536067219 sin53°=0.7986355100472928 sin54°=0.8090169943749474
sin55°=0.8191520442889918 sin56°=0.8290375725550417 sin57°=0.8386705679454239
sin58°=0.848048096156426 sin59°=0.8571673007021122 sin60°=0.8660254037844386
sin61°=0.8746197071393957 sin62°=0.8829475928589269 sin63°=0.8910065241883678
sin64°=0.898794046299167 sin65°=0.9063077870366499 sin66°=0.9135454576426009
sin67°=0.9205048534524404 sin68°=0.9271838545667873 sin69°=0.9335804264972017
sin70°=0.9396926207859083 sin71°=0.9455185755993167 sin72°=0.9510565162951535
sin73°=0.9563047559630354 sin74°=0.9612616959383189 sin75°=0.9659258262890683
sin76°=0.9702957262759965 sin77°=0.9743700647852352 sin78°=0.9781476007338057
sin79°=0.981627183447664 sin80°=0.984807753012208 sin81°=0.9876883405951378
sin82°=0.9902680687415704 sin83°=0.992546151641322 sin84°=0.9945218953682733
sin85°=0.9961946980917455 sin86°=0.9975640502598242 sin87°=0.9986295347545738
sin88°=0.9993908270190958 sin89°=0.9998476951563913
①列表(小力選取了10對(duì)數(shù)值);
②建立平面直角坐標(biāo)系(兩坐標(biāo)軸可視數(shù)值需要分別選取不同長(zhǎng)度做為單位長(zhǎng)度);
③描點(diǎn).在平面直角坐標(biāo)系xOy中,描出了以上表中各對(duì)對(duì)應(yīng)值為坐標(biāo)的點(diǎn);
④連線.根據(jù)描出的點(diǎn),畫出該函數(shù)的圖象;
(3)結(jié)合函數(shù)的圖象,寫出該函數(shù)的一條性質(zhì):y隨x(0°<x<90°)的增大而增大.