Question

Find the values of $\text{cot}\theta \text{and cosec}\theta$ in the figure given above.

• A. $2,\frac{5}{2}$
• B. $\frac{4}{3},\frac{5}{3}$
• C. $2,\frac{5}{4}$
• D. $\frac{5}{2},2$

Answer 1

The correct option is B

$\frac{4}{3},\frac{5}{3}$

For the angle $\theta$,

The opposite side is BC which has a length of 6 units
The adjacent side is AC which has a length of 8 units
The hypotenuse is AB which has a length of 10 units

$\text{cot}\theta =\frac{AC}{BC}=\frac{8}{6}=\frac{4}{3}\text{cosec}\theta =\frac{AB}{BC}=\frac{10}{6}=\frac{5}{3}$