Question

If $cot\theta =\frac{40}{9},$ find the values of $cosec\theta$ and $sin\theta .$

Answer 1

Consider the equation,

$\cot \theta =\frac{40}{9}$

${\cot }^2\theta ={\left(\frac{40}{9}\right)}^2=\frac{1600}{81}$

$1+{\cot }^2\theta =1+\frac{1600}{81}=\frac{1681}{81}$

$\cos e{c}^2\theta =\frac{1681}{81}$

$\cos ec\theta =\sqrt{\frac{1681}{81}}=\pm \frac{41}{81}$

$\cos ec\theta =\pm \frac{41}{81}$

$\sin \theta =\pm \frac{81}{41}$

Hence, this is the answer.