Question

If sinq=2/3 find the value of all the t-ratios

Answer 1

Answer:

$sin \: q = \frac{2}{3} \\ cos \: q = \sqrt{1 - {sin}^{2}q } \\ = \sqrt{1 - ( \frac{2}{3} )^{2} } \\ = \sqrt{ 1- \frac{4}{9} } \\ = \sqrt{ \frac{9 - 4}{9} } \\ = \sqrt{ \frac{5}{9} } \\ cos \: q = \frac{ \sqrt{5} }{3} \\ tan \: q = \frac{sin \: q}{cos \: q} = \frac{ \frac{2}{3} }{ \frac{ \sqrt{5} }{3} } \\ = \frac{2}{3} \times \frac{3 }{ \sqrt{5} } \\ tan \: q = \frac{2}{ \sqrt{5} } \\ sec \: q = \frac{1}{cos \: q} = \frac{1}{ \frac{ \sqrt{5} }{3} } = \frac{3}{ \sqrt{5} } \\ cot \: q = \frac{1}{tan \: q} = \frac{1}{ \frac{ 2 }{ \sqrt{5} } } = \frac{ \sqrt{5} }{ 2} \\ cosec \: q = \frac{1}{sin \: q} = \frac{1}{ \frac{ 2 }{ 3 } } = \frac{ 3 }{ 2}$