Question

Given $\sec \theta =\frac{13}{12}$, calculate all other trignometric ratios.

Answer 1

Let $△ABC$ be right angled triangle (right angled at $B$)

$\sec Q=\frac{AC}{AB}=\frac{13}{12}$

Let $AC=13x$ and $AB=12x$

$A{C}^2=A{B}^2+B{C}^2$

$B{C}^2=A{C}^2-A{B}^2$

$x^2=169-144$

$x^2=25$

$x=\sqrt{25}=5$

$\sin Q=\frac{BC}{AC}=\frac{5x}{13x}=\frac{5}{13}$

$\cos Q=\frac{AB}{AC}=\frac{12}{13}$

$\tan Q=\frac{BC}{AB}=\frac{5x}{12x}=\frac{5}{12}$

$\cot Q=\frac{1}{\tan Q}=\frac{1}{\frac{5}{12}}=\frac{12}{5}$

$\text{cosec}Q=\frac{AC}{BC}=\frac{13x}{5x}=\frac{13}{5}$