Question

Find the trigonometric ratios $\tan \theta$ and $\cos \theta$ of an angle $\theta$, which is in standard position, whose terminal arm passes through $(7,24)$

Answer 1

The terminal passes through the point $(7,24)$
i.e., $x=7$ and $y=24$
$\therefore$ The terminal arm is in the first quadrant.
$\therefore$ The ratios $\tan \theta$ and $\cos \theta$ are $+ve$
$\therefore r^2=x^2+y^2$
$=(7{)}^2+(24{)}^2$
$=49+576$
$=625$
$\therefore r=25$
$\therefore \tan \theta =\frac{y}{x}=\frac{24}{7}$
and $\cos \theta =\frac{x}{r}=\frac{7}{25}$