已知角α的终边在直线3x+4y=0上,求sinα,cosα,tanα的值.-数学

题目简介

已知角α的终边在直线3x+4y=0上,求sinα,cosα,tanα的值.-数学

题目详情

已知角α的终边在直线3x+4y=0上,求sinα,cosα,tanα的值.
题型:解答题难度:中档来源:不详

答案

∵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
=
(4t)2+(-3t)2
=5|t|

当t>0时,r=5t,
sinα=class="stub"y
r
=class="stub"-3t
5t
=-class="stub"3
5
,cosα=class="stub"x
r
=class="stub"4t
5t
=class="stub"4
5
,tanα=class="stub"y
x
=class="stub"-3t
4t
=-class="stub"3
4

当t<0时,r=-5t,sinα=class="stub"y
r
=class="stub"-3t
-5t
=class="stub"3
5

cosα=class="stub"x
r
=class="stub"4t
-5t
=-class="stub"4
5
,tanα=class="stub"y
x
=class="stub"-3t
4t
=-class="stub"3
4

综上可知,t>0时,sinα=-class="stub"3
5
,cosα=class="stub"4
5
,tanα=-class="stub"3
4

t<0时,sinα=class="stub"3
5
,cosα=-class="stub"4
5
,tanα=-class="stub"3
4

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