已知cos(α-π6)=35且α∈(5π3,13π6),求sinα的值.-数学

题目简介

已知cos(α-π6)=35且α∈(5π3,13π6),求sinα的值.-数学

题目详情

已知cos(α-
π
6
)=
3
5
α∈(
3
13π
6
)
,求sinα的值.
题型:解答题难度:中档来源:不详

答案

由于α∈(class="stub"5π
3
,class="stub"13π
6
)
,则α-class="stub"π
6
∈(class="stub"3π
2
,2π)
,∵cos(α-class="stub"π
6
)=class="stub"3
5
,∴sin(α-class="stub"π
6
)=-class="stub"4
5

sinα=sin[(α-class="stub"π
6
)+class="stub"π
6
]=sin(α-class="stub"π
6
)cosclass="stub"π
6
+cos(α-class="stub"π
6
)sinclass="stub"π
6

=-class="stub"4
5
×
3
2
+class="stub"3
5
×class="stub"1
2
=
3-4
3
10

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