题目内容
设Rt△ABC中,∠C=90°,∠A、∠B、∠C的对边分别为a、b、c,根据下列所给条件求∠B的四个三角函数值:(自己画图)
(1)a=1,c=2;(2)a=5,b=12.
(1)a=1,c=2;(2)a=5,b=12.
(1)∵a=1,c=2,
∴b=
=
,
∴sinB=
=
,
cosB=
=
,
tanB=
=
,
cotB=
=
=
;
(2)∵a=5,b=12.
∴c=
=13,
sinB=
=
,
cosB=
=
,
tanB=
=
,
cotB=
=
.
∴b=
c2-a2 |
3 |
∴sinB=
b |
c |
| ||
2 |
cosB=
a |
c |
1 |
2 |
tanB=
b |
a |
3 |
cotB=
a |
b |
1 | ||
|
| ||
3 |
(2)∵a=5,b=12.
∴c=
a2+b2 |
sinB=
b |
c |
12 |
13 |
cosB=
a |
c |
5 |
13 |
tanB=
b |
a |
12 |
5 |
cotB=
a |
b |
5 |
12 |
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