已知角α的终边在直线3x+4y=0上,求sinα,cosα,tanα的值.
问题描述:
已知角α的终边在直线3x+4y=0上,求sinα,cosα,tanα的值.
答
∵角α的终边在直线3x+4y=0上,
∴在角α的终边上任取一点P(4t,-3t)(t≠0),
则x=4t,y=-3t,r=
=
x2+y2
=5|t|,
(4t)2+(−3t)2
当t>0时,r=5t,
sinα=
=y r
=−−3t 5t
,cosα=3 5
=x r
=4t 5t
,tanα=4 5
=y x
=−−3t 4t
;3 4
当t<0时,r=-5t,sinα=
=y r
=−3t −5t
,3 5
cosα=
=x r
=−4t −5t
,tanα=4 5
=y x
=−−3t 4t
.3 4
综上可知,t>0时,sinα=−
,cosα=3 5
,tanα=−4 5
;3 4
t<0时,sinα=
,cosα=-3 5
,tanα=−4 5
.3 4