若z=sinθ-35+i(cosθ-45)是纯虚数,则tanθ的值为______.-数学

题目简介

若z=sinθ-35+i(cosθ-45)是纯虚数,则tanθ的值为______.-数学

题目详情

z=sinθ-
3
5
+i(cosθ-
4
5
)
是纯虚数,则tanθ的值为______.
题型:填空题难度:中档来源:不详

答案

z=sinθ-class="stub"3
5
+i(cosθ-class="stub"4
5
)
是纯虚数,
∴sinθ-class="stub"3
5
=0,
cosθ-class="stub"4
5
≠0,
∴sinθ =class="stub"3
5
,cosθ≠class="stub"4
5

∴cosθ=-class="stub"4
5

∴tanθ=-class="stub"3
4

故答案为:-class="stub"3
4

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