Question

From the figure, find the six trigonometric ratios of the angle $\theta$

Answer 1

From the fig, $AC=24$ and $BC=7$. By Pythagoras theorem
$A{B}^2=B{C}^2+C{A}^2=7^2+{24}^2=49+576=625$
$\therefore AB=\sqrt{625}=25$
We now use the three sides find the six trigonometric ratios of angle $\theta$
$\sin \theta =\frac{BC}{AB}=\frac{7}{25}cosec\theta =\frac{AB}{AC}=\frac{25}{7}$
$\cos \theta =\frac{AC}{AB}=\frac{24}{25}\sec \theta =\frac{AB}{AC}=\frac{25}{24}$
$\tan \theta =\frac{BC}{AC}=\frac{7}{24}\cot \theta =\frac{AC}{BC}=\frac{24}{7}$