若(-4,3)是角a终边上一点,求cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)的值
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![若(-4,3)是角a终边上一点,求cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)的值](/uploads/image/z/3709059-51-9.jpg?t=%E8%8B%A5%EF%BC%88-4%2C3%EF%BC%89%E6%98%AF%E8%A7%92a%E7%BB%88%E8%BE%B9%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E6%B1%82cos%28a-3%CF%80%29%2Atan%28a-4%CF%80%29%2Fsin%283%CF%80-a%29%2Acos%28a%2B5%CF%80%2F2%29%E7%9A%84%E5%80%BC)
若(-4,3)是角a终边上一点,求cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)的值
若(-4,3)是角a终边上一点,求cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)的值
若(-4,3)是角a终边上一点,求cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)的值
(-4,3)是角a终边上一点
得出
a是第二象限角
sina=3/5
cos(a-3π)=cos(a-3π+4π)=cos(a+π)=-cosa
tan(a-4π)=tana
sin(3π-a)=-sin(a-3π)=-sin(a-3π+4π)=-sin(a+π)=sina
cos(a+5π/2)=cos(a+5π/2-2π)=cos(a+π/2)=-sina
cos(a-3π)*tan(a-4π)/sin(3π-a)*cos(a+5π/2)
=[(-cosa)tana]/[sina*(-sina)]
=-sina/-sin²a
=1/sina
=5/3
因为点(-4,3)是角a终边上一点
所以角a为第二象限角
所以 原式=cos【-(3π-a)】*(-tana)/sina*(-sina)
=cosa*tana/sin^2a=1/sina
tana=-3/4
a=arctan(-3/4)=π-17.89=162.11度
cos(a-3π)=0.95
tan(a-4π)=-0.32
cos(a-3π)*tan(a-4π)=-0.304
sin(3π-a)=0.31
cos(a+5π/2)=-0.31
sin(3π-a)*cos(a+5π/2)=0.096
f(x)=-3.17