Question
Find all trigonometric functions of angle in standard position whose terminal arm passes through point $(3, – 4).$
✓
Answer
Let $\theta$ be the measure of the angle in standard position whose terminal arm passes through $P(3, -4).$
$\therefore x = 3$ and $y = -4$
$r = OP$
$=\sqrt{3^2+(-4)^2}$
$\quad=\sqrt{9+16}$
$=5$
$\sin \theta=\frac{y}{r}=-\frac{4}{5}$
$\cos \theta=\frac{x}{r}=\frac{3}{5}$
$\tan \theta=\frac{y}{x}=-\frac{4}{3}$
$\operatorname{cosec} \theta=\frac{r}{y}=-\frac{5}{4}$
$\sec \theta=\frac{r}{x}=\frac{5}{3}$
$\cot \theta=\frac{x}{y}=-\frac{3}{4}$
$\therefore x = 3$ and $y = -4$
$r = OP$
$=\sqrt{3^2+(-4)^2}$
$\quad=\sqrt{9+16}$
$=5$
$\sin \theta=\frac{y}{r}=-\frac{4}{5}$
$\cos \theta=\frac{x}{r}=\frac{3}{5}$
$\tan \theta=\frac{y}{x}=-\frac{4}{3}$
$\operatorname{cosec} \theta=\frac{r}{y}=-\frac{5}{4}$
$\sec \theta=\frac{r}{x}=\frac{5}{3}$
$\cot \theta=\frac{x}{y}=-\frac{3}{4}$
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