高中数学 三角函数 高中数学三角函数

\u9ad8\u4e2d\u6570\u5b66\u4e09\u89d2\u51fd\u6570\uff1f

\u56e0\u4e3a\u89d2\u03b1\u7ec8\u8fb9\u7ecf\u8fc7\u70b9(4,3)
\u6240\u4ee5sin\u03b1=4/5\uff0ccos\u03b1=3/5
\u56e0\u4e3a\u89d2\u03b2\u7ec8\u8fb9\u7ecf\u8fc7\u70b9(-7,-1)
\u6240\u4ee5sin\u03b2=1/5\u500d\u6839\u53f72=\u6839\u53f72/10\uff0ccos\u03b2=-7/5\u500d\u6839\u53f72=-7\u500d\u6839\u53f72/10
\u5219sin(\u03b1+\u03b2)=4/5*-7\u500d\u6839\u53f72/10+3/5*\u6839\u53f72/10
=-\u6839\u53f72/2
tan135=tan(65+70)=(tan65\u00b0+tan70\u00b0)/1-tan65\u00b0tan70\u00b0=-1
tan65\u00b0+tan70\u00b0=-(1-tan65\u00b0tan70\u00b0)
\u539f\u5f0f=-1

cos20cos40cos60cos80
=sin20cos20cos40cos60cos80/sin20
=1/2sin40cos40cos60cos80/sin20
=1/4sin80cos80cos60/sin20
=1/8sin160cos60/sin20
=1/8sin(180-160)cos60/sin20
=1/16
tan20+tan40-√3tan20tan40
=(sin20cos40+sin40cos20-√3sin20sin40)/(cos20cos40)
=(sin60-√3sin20sin40)/(cos20cos40)
=sin20(sin60-√3sin20sin40)/(sin20cos20cos40)
=2sin20(sin60-√3sin20sin40)/(sin40cos40)
=4sin160(sin60-√3sin20sin40)/sin80
=8cos80(sin60-√3sin20sin40)
=4√3sin10-4√3sin10[cos(40-20)-cos(40+20)]
=6√3sin10-4√3sin10cos20
=6√3sin10-2√3[sin(20+10)-sin(20-10)]
=8√3sin10-√3