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![](https://rs.olm.vn/images/avt/0.png?1311)
a) sin anpha = 2/3 => góc anpha = 42o
cos 42o = 0,743
tan 42o = 0,9
cot 42o = 1/tan 42o = 1/0,9 = 1,111
b) tan anpha + cot anpha = 3
<=> tan anpha + 1/tan anpha = 3
<=> tan2 anpha = 2
<=> tan anpha = \(\sqrt{2}\)
=> góc anpha = 55o
Ta có: a = sin 55o . cos 55o
<=> a = 0,469
![](https://rs.olm.vn/images/avt/0.png?1311)
a: sin a=1/2
=>a=30 độ
b: cos a=2/3
=>\(a\simeq48^0\)
c: tan a=4/5
=>\(a\simeq39^0\)
d: \(cota=\dfrac{3}{4}\)
=>tan a=4/3
=>\(a\simeq53^0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1:
a: sin a=căn 3/2
\(cosa=\sqrt{1-sin^2a}=\sqrt{1-\dfrac{3}{4}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}\)
\(tana=\dfrac{\sqrt{3}}{2}:\dfrac{1}{2}=\sqrt{3}\)
cot a=1/tan a=1/căn 3
b: \(tana=2\)
=>cot a=1/tan a=1/2
\(1+tan^2a=\dfrac{1}{cos^2a}\)
=>\(\dfrac{1}{cos^2a}=5\)
=>cos^2a=1/5
=>cosa=1/căn 5
\(sina=\sqrt{1-cos^2a}=\sqrt{\dfrac{4}{5}}=\dfrac{2}{\sqrt{5}}\)
c: \(cosa=\sqrt{1-\left(\dfrac{5}{13}\right)^2}=\dfrac{12}{13}\)
tan a=5/13:12/13=5/12
cot a=1:5/12=12/5
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: sin a=2/3
=>cos^2a=1-(2/3)^2=5/9
=>\(cosa=\dfrac{\sqrt{5}}{3}\)
\(tana=\dfrac{2}{3}:\dfrac{\sqrt{5}}{3}=\dfrac{2}{\sqrt{5}}\)
\(cota=1:\dfrac{2}{\sqrt{5}}=\dfrac{\sqrt{5}}{2}\)
b: cos a=1/5
=>sin^2a=1-(1/5)^2=24/25
=>\(sina=\dfrac{2\sqrt{6}}{5}\)
\(tana=\dfrac{2\sqrt{6}}{5}:\dfrac{1}{5}=2\sqrt{6}\)
\(cota=\dfrac{1}{2\sqrt{6}}=\dfrac{\sqrt{6}}{12}\)
c: cot a=1/tana=1/2
\(1+tan^2a=\dfrac{1}{cos^2a}\)
=>1/cos^2a=1+4=5
=>cos^2a=1/5
=>cosa=1/căn 5
\(sina=\sqrt{1-cos^2a}=\dfrac{2}{\sqrt{5}}\)
Bài 2:
cos a=0,8
tan a=0,6/0,8=3/4
cot a=4/3