Question

Cho sin a=1:2.hãy tính cos a và tan a

Answer 1

\(\sin\alpha=\dfrac{1}{2}\)

Ta có:

\(\sin^2\alpha+\cos^2\alpha=1\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^2+\cos^2\alpha=1\)

\(\Leftrightarrow\cos\alpha=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\dfrac{\sqrt{3}}{2}\)

`@`\(\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}\)

\(\Leftrightarrow\tan\alpha=\dfrac{1}{2}:\dfrac{\sqrt{3}}{2}=\dfrac{\sqrt{3}}{3}\)

Answer 2

Ta có:

sin²a + cos²a = 1

Suy ra: cos²a = 1 - sin²a

= 1 - (1/2)²

= 1 - 1/4

= 3/4

Suy ra cos a = căn(3)/2

Suy ra tan a = sin a / cos a

= căn(3)/2 /1/2

= căn(3)