以123.(312x+203)为弧度的四个三角函数图像对比解析

以123/(312x+203)为弧度的四个三角函数图像对比主要内容：本文主要介绍以123/(312x+203)为弧度的四个三角函数，即y=sin[123/(312x+203)]，y=cos[123/(312x+203)]，y=tan[123/(312x+203)]，y=cgt[123/(312x+203))]的函数性质及图像示意图。以eq\f(123,312x+203)为弧度的四个三角函数图像对比※.正弦函数y=sineq\f(123,312x+203)的图像☆.函数的定义域：因为y=sineq\f(123,312x+203)，正弦函数的定义域为全体实数，又y₁=eq\f(123,312x+203)自变量x在分母中，则有312x+203≠0，即x≠-eq\f(203,312)≈-0.65，所以函数的定义域为：(-∞,-eq\f(203,312))∪(-eq\f(203,312),+∞)。☆.函数的五点图：以eq\f(123,312x+203)∈[-2π,2π]上为例：x-0.71-0.72-0.73-0.75-1.910.60eq\f(123,312x+203)-2π-1.75π-1.5π-1.25π-π-0.75πsineq\f(123,312x+203)00.70710.7070-0.707x-0.90-1.15-1.910.60-0.15-0.40eq\f(123,312x+203)-0.5π-0.25π-0.1π0.1π0.25π0.5πsineq\f(123,312x+203)-1-0.707-0.310.310.7071x-0.48-0.53-0.55-0.57-0.58-0.59eq\f(123,312x+203)0.75ππ1.25π1.5π1.75π2πsineq\f(123,312x+203)0.7070-0.707-1-0.7070☆.函数的示意图以eq\f(123,312x+203)∈[-2π,2π]上为例:y=sineq\f(123,312x+203)。y(-0.73,1)(-0.40,1)(-0.15,0.707)(-0.75,0.707)(0.60,0.31)(-1.91,-0.31)x(-1.15,-0.707)(-1.91,-0.707)(-0.90,-1)(-0.75,-1)※.余弦函数y=coseq\f(123,312x+203)的图像☆.函数的定义域：因为y=coseq\f(123,312x+203)，余弦函数的定义域为全体实数，又y₁=eq\f(123,312x+203)自变量x在分母中，则有312x+203≠0，即x≠-eq\f(203,312)≈-0.65，所以函数的定义域为：(-∞,-eq\f(203,312))∪(-eq\f(203,312),+∞)。☆.函数的五点图：以eq\f(123,312x+203)∈[-2π,2π]上为例：x-0.71-0.72-0.73-0.75-1.910.60eq\f(123,312x+203)-2π-1.75π-1.5π-1.25π-π-0.75πcoseq\f(123,312x+203)10.7070-0.707-1-0.707x-0.90-1.15-1.910.60-0.15-0.40eq\f(123,312x+203)-0.5π-0.25π-0.1π0.1π0.25π0.5πcoseq\f(123,312x+203)0-0.7070.950.950.7071x-0.48-0.53-0.55-0.57-0.58-0.59eq\f(123,312x+203)0.75ππ1.25π1.5π1.75π2πcoseq\f(123,312x+203)-0.707-1-0.70700.7071☆.函数的示意图以eq\f(123,312x+203)∈[-2π,2π]上为例：y=coseq\f(123,312x+203)。(-1.91,0.95)(-0.71,1)(-0.59,1)(0.60,0.95)(-0.72,0.707)(-0.15,0.707)x(-1.15,-0.707)(-1.91,-1)(-0.53,-1)※.正切函数y=taneq\f(123,312x+203)的图像☆.函数的定义域：因为y=taneq\f(123,312x+203)，要求eq\f(123,312x+203)≠kπ+eq\f(π,2)，即：x≠eq\f(246,312*(2k+1)π)-eq\f(203,312)，又y₁=eq\f(123,312x+203)有312x+203≠0，即x≠-eq\f(203,312)≈-0.65，所以函数的定义域为：{x|x≠{eq\f(246,312*(2k+1)π)-eq\f(203,312),，x∈R，k∈Z}。☆.函数的五点图：以eq\f(123,312x+203)∈[-2.5π，2.5π]上为例：x-0.70-0.71-0.73-0.74-0.78-0.86eq\f(123,312x+203)-2.4π-2π-1.6π-1.4π-π-0.6πtaneq\f(123,312x+203)-3.0803.08-3.0803.08x-0.96-1.15-1.910.60-0.15-0.34eq\f(123,312x+203)-0.4π-0.25π-0.1π0.1π0.25π0.4πtaneq\f(123,312x+203)-3.08-1-0.320.3213.08x-0.44-0.53-0.56-0.57-0.59-0.60eq\f(123,312x+203)0.6ππ1.4π1.6π2π2.4πtaneq\f(123,312x+203)-3.0803.08-3.0803.08☆.函数的五点图：以eq\f(123,312x+203)∈[-2.5π，2.5π]上为例：y=taneq\f(123,312x+203)y(-0.86,3.08)(-0.34,3.08) (-0.15,1)(0.60,0.32)x(-1.91,-0.32)(-1.15,-1)(-0.96,-3.08)(-0.44,-3.08)※.余切函数y=ctgeq\f(123,312x+203)的图像☆.函数的定义域：因为y=ctgeq\f(123,312x+203)，余切函数的定义域要求eq\f(123,312x+203)≠kπ+π，即：x≠eq\f(123,312*(k+1)π)-eq\f(203,312),又y₁=eq\f(123,312x+203)自变量x在分母中，则有312x+203≠0，即x≠-eq\f(203,312)≈-0.65，所以函数的定义域为：{x|x≠eq\f(123,312*(k+1)π)-eq\f(203,312)，x∈R，k∈Z}。☆.函数的五点图：以eq\f(123,312x+203)∈[-2π，2π]上为例：x-0.72-0.73-0.76-0.79-0.90-1.15eq\f(123,312x+203)-1.9π-1.5π-1.1π-0.9π-0.5π-0.25πctgeq\f(123,312x+203)3.080-3.083.080-1x-1.910.60-0.15-0.40-0.48-0.51eq\f(123,312x+203)-0.1π0.1π0.25π0.5π0.75π0.9πctgeq\f(123,312x+203)-3.083.0810-1-3.08x-0.54-0.55-0.57-0.58-0.58eq\f(123,312x+203)1.1π1.25π1.5π1.75π1.9πctgeq\f(123,312x+203)3.08101-3.08☆.函数的五点图：以eq\f(123,312x+203)∈[-2π，2π]上为例：y=ctgeq\f(123,312x+203)， y(-