Question

If sin theta =1/root 2 find other trigonometry ratios

Answer 1

$sin \theta = \frac{1}{ \sqrt{2} } \\ cosec \theta = \frac{1}{sin \theta} = \sqrt{2} \\ \\ cos \theta = \sqrt{1 - {sin}^{2} \theta } \\ = \sqrt{1 - \frac{1}{2} } \\ = \frac{1}{ \sqrt{2} } \\ sec \theta = \frac{1}{cos \theta} = \sqrt{2} \\ \\ tan \theta = \frac{sin \theta}{cos \theta} = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } } = 1 \\ cot \theta = \frac{1}{tan \theta} = 1$