Question

tanx = SQRT3/3 and cosx = SQRT3/2 what is sin, cot, and sec?

Answer 1

Well \[\tan(x) = \frac{\sin(x)}{\cos(x)}\]. This means that \[\sin(x)= \tan(x)\cos(x) = \frac{\sqrt{3}}{3}*\frac{\sqrt{3}}{2} = \frac{ 1 }{ 2 }\]

Answer 2

\[\sec(x) = \frac{ 1 }{ \cos(x) } = \frac{ 1 }{ \frac{ \sqrt{3} }{ 2 } } = \frac{ 2 }{ \sqrt{3} } = \frac{ 2\sqrt{3} }{ 3 }\]

Answer 3

\[\cot(x) = \frac{ 1 }{ \tan(x) } = \frac{ 1 }{ \frac{ \sqrt{3} }{ 3 } } = \frac{ 3 }{ \sqrt{3} } = \frac{ 3\sqrt{3} }{ 3 }\]