下列不等式正确的是()A.sin40°<sin1030°B.tan(-13π4)>tan(-16π5)C.sin89°>tan46°D.sinπ5<cos(-π4)-数学

题目简介

下列不等式正确的是()A.sin40°<sin1030°B.tan(-13π4)>tan(-16π5)C.sin89°>tan46°D.sinπ5<cos(-π4)-数学

题目详情

下列不等式正确的是(  )
A.sin40°<sin1030°B.tan(-
13π
4
)>tan(-
16π
5
)
C.sin89°>tan46°D.sin
π
5
<cos(-
π
4
)
题型:单选题难度:中档来源:不详

答案

A.sin1030°=sin(1030°-360°×3)=-sin50°<0,A错.
B.tan(-class="stub"13π
4
)
=tan(-class="stub"13π
4
+3π)
=tan(-class="stub"π
4
)
tan(-class="stub"16π
5
)
=tan(-class="stub"16π
5
+3π)
=tan(-class="stub"π
5
)

-class="stub"π
2
<-class="stub"π
4
<-class="stub"π
5
<0
,∴tan(-class="stub"π
4
)<tan(-class="stub"π
5
)
,即tan(-class="stub"13π
4
)<tan(-class="stub"16π
5
)
.B错.
C.sin89°<1,tan46°>1,sin89°<tan46°.C错.
D.cos(-class="stub"π
4
)
=cosclass="stub"π
4
=sin(class="stub"π
2
-class="stub"π
4
)
=sinclass="stub"π
4
0<class="stub"π
5
<class="stub"π
4
<class="stub"π
2
,∴sinclass="stub"π
5
<sinclass="stub"π
4
sinclass="stub"π
5
<cos(-class="stub"π
4
)
D正确.
故选D.

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