arcsiny=arcsinx+arcsinc如何化解成y= y=arcsinx图像怎么画
arcsiny=arcsinx c\u600e\u4e48\u5316\u7b80\uff1farcsiny=arcsinx
\u54ea\u6709c?
...
arcsiny=arcsinx+C\uff1f
y = sin(arcsinx + C)
\u4ee4C=arcsinD,\u5219D=sinC\uff0c\u7136\u540e\u7528sin+\u5c55\u5f00\u4e3a
y = sin(arcsinx + arcsinD)
= sin(arcsinx)*cos(arcsinD) + cos(arcsinx)*sin(arcsinD)
= x * \u221a(1-D²) + \u221a(1-x²) * D
=x * \u221a[1-(sinC)²] + \u221a(1-x²) *sinC
\u221a\u662f\u6839\u53f7\u4e0b\uff0c\u6ce8\u610f\u62ec\u53f7\uff0c\u4ee5\u4e0a\u3002
y=arcsinx\u53cd\u6b63\u5f26\u51fd\u6570\uff0c\u56fe\u50cf\u8be6\u7ec6\u89c1\u4e0b\u56fe\uff1a
\u53cd\u6b63\u5f26\u51fd\u6570\uff08\u53cd\u4e09\u89d2\u51fd\u6570\u4e4b\u4e00\uff09\u4e3a\u6b63\u5f26\u51fd\u6570y=sinx\uff08x\u2208[-½\u03c0,½\u03c0]\uff09\u7684\u53cd\u51fd\u6570\uff0c\u8bb0\u4f5cy=arcsinx\u6216siny=x\uff08x\u2208[-1,1]\uff09\u3002\u7531\u539f\u51fd\u6570\u7684\u56fe\u50cf\u548c\u5b83\u7684\u53cd\u51fd\u6570\u7684\u56fe\u50cf\u5173\u4e8e\u4e00\u4e09\u8c61\u9650\u89d2\u5e73\u5206\u7ebf\u5bf9\u79f0\u53ef\u77e5\u6b63\u5f26\u51fd\u6570\u7684\u56fe\u50cf\u548c\u53cd\u6b63\u5f26\u51fd\u6570\u7684\u56fe\u50cf\u4e5f\u5173\u4e8e\u4e00\u4e09\u8c61\u9650\u89d2\u5e73\u5206\u7ebf\u5bf9\u79f0\u3002
\u5728\u6570\u5b66\u4e2d\uff0c\u53cd\u4e09\u89d2\u51fd\u6570\uff08antitrigonometric functions\uff0c\u5076\u5c14\u4e5f\u79f0\u4e3a\u5f13\u5f62\u51fd\u6570\uff08arcus functions\uff09\uff0c\u53cd\u5411\u51fd\u6570\uff08reverse function\uff09\u6216\u73af\u5f62\u51fd\u6570\uff08cyclometric functions\uff09\uff09\u662f\u4e09\u89d2\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff08\u5177\u6709\u9002\u5f53\u7684\u9650\u5236\u57df\uff09\u3002
\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u4eec\u662f\u6b63\u5f26\uff0c\u4f59\u5f26\uff0c\u6b63\u5207\uff0c\u4f59\u5207\uff0c\u6b63\u5272\u548c\u8f85\u52a9\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff0c\u5e76\u4e14\u7528\u4e8e\u4ece\u4efb\u4f55\u4e00\u4e2a\u89d2\u5ea6\u7684\u4e09\u89d2\u6bd4\u83b7\u5f97\u4e00\u4e2a\u89d2\u5ea6\u3002 \u53cd\u4e09\u89d2\u51fd\u6570\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5de5\u7a0b\uff0c\u5bfc\u822a\uff0c\u7269\u7406\u548c\u51e0\u4f55\u3002
\u6269\u5c55\u8d44\u6599
\u539f\u51fd\u6570\uff1a
\u7528\u5206\u90e8\u79ef\u5206\u6cd5\uff1a
\u222b arcsinxdx
=xarcsinx-\u222bxdx(1-x^2)^(-1/2)
=xarcsinx+\u222b(1-x^2)^(-1/2)d(1-x^2)
=xarcsinx+2(1-x^2)^(1/2)
arcsinx\u662fsinx\u7684\u53cd\u51fd\u6570\uff0c\u5982\u679csinx=y\uff0c\u90a3\u4e48arcsiny=x\u56e0\u4e3asin\u662f\u5468\u671f\u51fd\u6570\uff0c\u4e3a\u4e86\u4f7f\u5f97\u51fd\u6570\u6709\u552f\u4e00\u503c\uff0carcsinx\u7684\u53d6\u503c\u8303\u56f4\u662f(-90\uff0c90]\u5ea6\u4e4b\u95f4\u3002arcsin0=0\uff0carcsin1=90\u5ea6\u3002
sinx\u8868\u793a\u4e00\u4e2a\u6570\u5b57\uff0c\u5176\u4e2d\u7684X\u662f\u4e00\u4e2a\u89d2\u5ea6\u3002arcsinx\u8868\u793a\u4e00\u4e2a\u89d2\u5ea6\uff0c\u5176\u4e2d\u7684X\u662f\u4e00\u4e2a\u6570\u5b57\uff0c-1<=X<=1\u3002arcsinx\u8868\u793a\u7684\u89d2\u5ea6\u5c31\u662f\u6307\uff0c\u6b63\u5f26\u503c\u4e3aX\u7684\u90a3\u4e2a\u89d2\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u53cd\u6b63\u5f26\u51fd\u6570
= sin(arcsinx)*cos(arcsinc) + cos(arcsinx)*sin(arcsinc)
= x * √(1-c²) + √(1-x²) * c
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