以57.(49x+15)为弧度的三角函数图像对比

以57/(49x+15)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57/(49x+15)为弧度的四个三角函数，即y=sin[57/(49x+15)]，y=cos[57/(49x+15)]，y=tan[57/(49x+15)]，y=cgt[57/(49x+15))]的函数性质及图像示意图。以eq\f(57,49x+15)为弧度的四个三角函数图像对比※.正弦函数y=sineq\f(57,49x+15)的图像☆.函数的定义域：因为y=sineq\f(57,49x+15)，正弦函数的定义域为全体实数，又y₁=eq\f(57,49x+15)自变量x在分母中，则有49x+15≠0，即x≠-eq\f(15,49)≈-0.31，所以函数的定义域为：(-∞,-eq\f(15,49))∪(-eq\f(15,49),+∞)。☆.函数的五点图：以eq\f(57,49x+15)∈[-2π,2π]上为例：x-0.49-0.52-0.55-0.60-4.013.40eq\f(57,49x+15)-2π-1.75π-1.5π-1.25π-π-0.75πsineq\f(57,49x+15)00.70710.7070-0.707x-1.05-1.79-4.013.401.170.43eq\f(57,49x+15)-0.5π-0.25π-0.1π0.1π0.25π0.5πsineq\f(57,49x+15)-1-0.707-0.310.310.7071x0.190.06-0.01-0.06-0.09-0.12eq\f(57,49x+15)0.75ππ1.25π1.5π1.75π2πsineq\f(57,49x+15)0.7070-0.707-1-0.7070☆.函数的示意图以eq\f(57,49x+15)∈[-2π,2π]上为例:y=sineq\f(57,49x+15)。y(-0.55,1)(0.43,1)(1.17,0.707)(-0.60,0.707)(3.40,0.31)(-4.01,-0.31)x(-1.79,-0.707)(-4.01,-0.707)(-1.05,-1)(-0.60,-1)※.余弦函数y=coseq\f(57,49x+15)的图像☆.函数的定义域：因为y=coseq\f(57,49x+15)，余弦函数的定义域为全体实数，又y₁=eq\f(57,49x+15)自变量x在分母中，则有49x+15≠0，即x≠-eq\f(15,49)≈-0.31，所以函数的定义域为：(-∞,-eq\f(15,49))∪(-eq\f(15,49),+∞)。☆.函数的五点图：以eq\f(57,49x+15)∈[-2π,2π]上为例：x-0.49-0.52-0.55-0.60-4.013.40eq\f(57,49x+15)-2π-1.75π-1.5π-1.25π-π-0.75πcoseq\f(57,49x+15)10.7070-0.707-1-0.707x-1.05-1.79-4.013.401.170.43eq\f(57,49x+15)-0.5π-0.25π-0.1π0.1π0.25π0.5πcoseq\f(57,49x+15)0-0.7070.950.950.7071x0.190.06-0.01-0.06-0.09-0.12eq\f(57,49x+15)0.75ππ1.25π1.5π1.75π2πcoseq\f(57,49x+15)-0.707-1-0.70700.7071☆.函数的示意图以eq\f(57,49x+15)∈[-2π,2π]上为例：y=coseq\f(57,49x+15)。(-4.01,0.95)(-0.49,1)(-0.12,1)(3.40,0.95)(-0.52,0.707)(1.17,0.707)x(-1.79,-0.707)(-4.01,-1)(0.06,-1)※.正切函数y=taneq\f(57,49x+15)的图像☆.函数的定义域：因为y=taneq\f(57,49x+15)，要求eq\f(57,49x+15)≠kπ+eq\f(π,2)，即：x≠eq\f(114,49*(2k+1)π)-eq\f(15,49)，又y₁=eq\f(57,49x+15)有49x+15≠0，即x≠-eq\f(15,49)≈-0.31，所以函数的定义域为：{x|x≠{eq\f(114,49*(2k+1)π)-eq\f(15,49),，x∈R，k∈Z}。☆.函数的五点图：以eq\f(57,49x+15)∈[-2.5π，2.5π]上为例：x-0.46-0.49-0.54-0.57-0.68-0.92eq\f(57,49x+15)-2.4π-2π-1.6π-1.4π-π-0.6πtaneq\f(57,49x+15)-3.0803.08-3.0803.08x-1.23-1.79-4.013.401.170.62eq\f(57,49x+15)-0.4π-0.25π-0.1π0.1π0.25π0.4πtaneq\f(57,49x+15)-3.08-1-0.320.3213.08x0.310.06-0.04-0.07-0.12-0.15eq\f(57,49x+15)0.6ππ1.4π1.6π2π2.4πtaneq\f(57,49x+15)-3.0803.08-3.0803.08☆.函数的五点图：以eq\f(57,49x+15)∈[-2.5π，2.5π]上为例：y=taneq\f(57,49x+15)y(-0.92,3.08)(0.62,3.08) (1.17,1)(3.40,0.32)x(-4.01,-0.32)(-1.79,-1)(-1.23,-3.08)(0.31,-3.08)※.余切函数y=ctgeq\f(57,49x+15)的图像☆.函数的定义域：因为y=ctgeq\f(57,49x+15)，余切函数的定义域要求eq\f(57,49x+15)≠kπ+π，即：x≠eq\f(57,49*(k+1)π)-eq\f(15,49),又y₁=eq\f(57,49x+15)自变量x在分母中，则有49x+15≠0，即x≠-eq\f(15,49)≈-0.31，所以函数的定义域为：{x|x≠eq\f(57,49*(k+1)π)-eq\f(15,49)，x∈R，k∈Z}。☆.函数的五点图：以eq\f(57,49x+15)∈[-2π，2π]上为例：x-0.50-0.55-0.64-0.72-1.05-1.79eq\f(57,49x+15)-1.9π-1.5π-1.1π-0.9π-0.5π-0.25πctgeq\f(57,49x+15)3.080-3.083.080-1x-4.013.401.170.430.190.11eq\f(57,49x+15)-0.1π0.1π0.25π0.5π0.75π0.9πctgeq\f(57,49x+15)-3.083.0810-1-3.08x0.03-0.01-0.06-0.09-0.11eq\f(57,49x+15)1.1π1.25π1.5π1.75π1.9πctgeq\f(57,49x+15)3.08101-3.08☆.函数的五点图：以eq\f(57,49x+15)∈[-2π，2π]上为例：y=ctgeq\f(57,49x+15)， y(-0.72,3.