Question

If sin α =

√3

2

, find cos α, tan α
​

Answer 1

Answer:

$\cos(a) = \sqrt{1 - {( \sin(a) })^{2} } \\ = \sqrt{1 - \frac{ { (\sqrt{3}) }^{2} }{ {2}^{2} } } \: \: \: \: \: \\\ = \sqrt{1 - \frac{3}{4} } \\ = \sqrt{ \frac{1}{4} } \: \: \: \: \: \: \: \\ = \sqrt{ \frac{ {1}^{2} }{ {2}^{2} } } \\ = \frac{1}{2 } \\ therefore \: \cos(a \: ) = \frac{1}{2 } \\ we \: know \: \tan(a) = \frac{ \sin(a) }{ \cos(a) } \\ therefore \: \tan(a) = \frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} } = \sqrt{3}$

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