已知角α的终边过点P(2t,-3t)(t≠0),求sinα,cosα,tanα的值.-数学

题目简介

已知角α的终边过点P(2t,-3t)(t≠0),求sinα,cosα,tanα的值.-数学

题目详情

已知角α的终边过点P(2t,-3t)(t≠0),求sinα,cosα,tanα的值.
题型:解答题难度:中档来源:不详

答案

已知角α的终边过点P(2t,-3t)(t≠0),故有x=2t,y=-3t,r=
13
|t|.
当t>0时,r=
13
t,故sinα=class="stub"y
r
=-class="stub"3
13
=-
3
13
13
,cosα=class="stub"x
r
=class="stub"2t
13
•t
=
2
13
13
,tanα=class="stub"y
x
=-class="stub"3
2

当t<0时,r=-
13
t,sinα=class="stub"y
r
=class="stub"3
13
=
3
13
13
,cosα=class="stub"x
r
=-
2
13
13
,tanα=class="stub"y
x
=-class="stub"3
2

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