设α为第一象限的角,且sinα=3/5,求(sin(π+α)+cos(5π-α))/(sin(α-6π)+2cos(2π+α))
问题描述:
设α为第一象限的角,且sinα=3/5,求(sin(π+α)+cos(5π-α))/(sin(α-6π)+2cos(2π+α))
答
α为第一象限的角,sinα=3/5,则cosα=4/5
(sin(π+α)+cos(5π-α))/(sin(α-6π)+2cos(2π+α))
=(-sinα-cosα)/(sinα+2cosα)
=(-3/5-4/5)/(3/5+2*4/5)
=(-7/5)/(11/5)
=-7/11