详细解读以192.(144x+193)为弧度的四个三角函数图像对比

以192/(144x+193)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192/(144x+193)为弧度的四个三角函数，即y=sin[192/(144x+193)]，y=cos[192/(144x+193)]，y=tan[192/(144x+193)]，y=cgt[192/(144x+193))]的函数性质及图像示意图。以eq\f(192,144x+193)为弧度的四个三角函数图像对比※.正弦函数y=sineq\f(192,144x+193)的图像☆.函数的定义域：因为y=sineq\f(192,144x+193)，正弦函数的定义域为全体实数，又y₁=eq\f(192,144x+193)自变量x在分母中，则有144x+193≠0，即x≠-eq\f(193,144)≈-1.34，所以函数的定义域为：(-∞,-eq\f(193,144))∪(-eq\f(193,144),+∞)。☆.函数的五点图：以eq\f(192,144x+193)∈[-2π,2π]上为例：x-1.55-1.58-1.62-1.68-5.582.90eq\f(192,144x+193)-2π-1.75π-1.5π-1.25π-π-0.75πsineq\f(192,144x+193)00.70710.7070-0.707x-2.19-3.04-5.582.900.36-0.49eq\f(192,144x+193)-0.5π-0.25π-0.1π0.1π0.25π0.5πsineq\f(192,144x+193)-1-0.707-0.310.310.7071x-0.77-0.92-1.00-1.06-1.10-1.13eq\f(192,144x+193)0.75ππ1.25π1.5π1.75π2πsineq\f(192,144x+193)0.7070-0.707-1-0.7070☆.函数的示意图以eq\f(192,144x+193)∈[-2π,2π]上为例:y=sineq\f(192,144x+193)。y(-1.62,1)(-0.49,1)(0.36,0.707)(-1.68,0.707)(2.90,0.31)(-5.58,-0.31)x(-3.04,-0.707)(-5.58,-0.707)(-2.19,-1)(-1.68,-1)※.余弦函数y=coseq\f(192,144x+193)的图像☆.函数的定义域：因为y=coseq\f(192,144x+193)，余弦函数的定义域为全体实数，又y₁=eq\f(192,144x+193)自变量x在分母中，则有144x+193≠0，即x≠-eq\f(193,144)≈-1.34，所以函数的定义域为：(-∞,-eq\f(193,144))∪(-eq\f(193,144),+∞)。☆.函数的五点图：以eq\f(192,144x+193)∈[-2π,2π]上为例：x-1.55-1.58-1.62-1.68-5.582.90eq\f(192,144x+193)-2π-1.75π-1.5π-1.25π-π-0.75πcoseq\f(192,144x+193)10.7070-0.707-1-0.707x-2.19-3.04-5.582.900.36-0.49eq\f(192,144x+193)-0.5π-0.25π-0.1π0.1π0.25π0.5πcoseq\f(192,144x+193)0-0.7070.950.950.7071x-0.77-0.92-1.00-1.06-1.10-1.13eq\f(192,144x+193)0.75ππ1.25π1.5π1.75π2πcoseq\f(192,144x+193)-0.707-1-0.70700.7071☆.函数的示意图以eq\f(192,144x+193)∈[-2π,2π]上为例：y=coseq\f(192,144x+193)。(-5.58,0.95)(-1.55,1)(-1.13,1)(2.90,0.95)(-1.58,0.707)(0.36,0.707)x(-3.04,-0.707)(-5.58,-1)(-0.92,-1)※.正切函数y=taneq\f(192,144x+193)的图像☆.函数的定义域：因为y=taneq\f(192,144x+193)，要求eq\f(192,144x+193)≠kπ+eq\f(π,2)，即：x≠eq\f(384,144*(2k+1)π)-eq\f(193,144)，又y₁=eq\f(192,144x+193)有144x+193≠0，即x≠-eq\f(193,144)≈-1.34，所以函数的定义域为：{x|x≠{eq\f(384,144*(2k+1)π)-eq\f(193,144),，x∈R，k∈Z}。☆.函数的五点图：以eq\f(192,144x+193)∈[-2.5π，2.5π]上为例：x-1.52-1.55-1.61-1.64-1.76-2.05eq\f(192,144x+193)-2.4π-2π-1.6π-1.4π-π-0.6πtaneq\f(192,144x+193)-3.0803.08-3.0803.08x-2.40-3.04-5.582.900.36-0.28eq\f(192,144x+193)-0.4π-0.25π-0.1π0.1π0.25π0.4πtaneq\f(192,144x+193)-3.08-1-0.320.3213.08x-0.63-0.92-1.04-1.08-1.13-1.16eq\f(192,144x+193)0.6ππ1.4π1.6π2π2.4πtaneq\f(192,144x+193)-3.0803.08-3.0803.08☆.函数的五点图：以eq\f(192,144x+193)∈[-2.5π，2.5π]上为例：y=taneq\f(192,144x+193)y(-2.05,3.08)(-0.28,3.08) (0.36,1)(2.90,0.32)x(-5.58,-0.32)(-3.04,-1)(-2.40,-3.08)(-0.63,-3.08)※.余切函数y=ctgeq\f(192,144x+193)的图像☆.函数的定义域：因为y=ctgeq\f(192,144x+193)，余切函数的定义域要求eq\f(192,144x+193)≠kπ+π，即：x≠eq\f(192,144*(k+1)π)-eq\f(193,144),又y₁=eq\f(192,144x+193)自变量x在分母中，则有144x+193≠0，即x≠-eq\f(193,144)≈-1.34，所以函数的定义域为：{x|x≠eq\f(192,144*(k+1)π)-eq\f(193,144)，x∈R，k∈Z}。☆.函数的五点图：以eq\f(192,144x+193)∈[-2π，2π]上为例：x-1.56-1.62-1.73-1.81-2.19-3.04eq\f(192,144x+193)-1.9π-1.5π-1.1π-0.9π-0.5π-0.25πctgeq\f(192,144x+193)3.080-3.083.080-1x-5.582.900.36-0.49-0.77-0.87eq\f(192,144x+193)-0.1π0.1π0.25π0.5π0.75π0.9πctgeq\f(192,144x+193)-3.083.0810-1-3.08x-0.95-1.00-1.06-1.10-1.12eq\f(192,144x+193)1.1π1.25π1.5π1.75π1.9πctgeq\f(192,144x+193)3.08101-3.08☆.函数的五点图：以eq\f(192,144x+193)∈[-2π，2π]上为例：y=ctgeq\f(192,144x+193)， y(-