Question

Find the values of $cot\theta andcosec\theta$ 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 $\frac{4}{3},\frac{5}{3}$

In the given triangle ABC, 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.

$\text{So,}cot\theta =\frac{adjacentside}{oppositeside}=\frac{AC}{BC}=\frac{8}{6}=\frac{2\times 4}{2\times 3}=\frac{4}{3}cosec\theta =\frac{hypotenuse}{oppositeside}=\frac{AB}{BC}=\frac{10}{6}=\frac{2\times 5}{2\times 3}=\frac{5}{3}$