Question

given sec q=13/12 calculate all other trignometric ratios

Answer 1

Given $\sec q=\frac{13}{12}$.

$\cos q=\frac{11}{13}$

Use the identity,

$\tan^2 q=\sec^2 q-1\\ \tan^2 q=(\frac{13}{12})^2-1 \\ \tan^2 q=\frac{13^2-12^2}{12^2}\\ \tan^2 q=\frac{5^2}{12^2}\\ \tan q=\frac{5}{12}$

$\sin q=\sqrt{1-(\frac{12}{13}^2) } \\ \sin q=\frac{5}{13} \\ \csc q=\frac{13}{5} \\ \cot q=\frac{12}{5}$