Question

Find the value of csc theta, if cos =-3/5; 90 degrees < theta < 180 degrees

Answer 1

Answer:$\frac{5}{4}$

Step-by-step explanation:

Given

$\cos \theta =\frac{-3}{5}$

and $\theta$  lies between

$90^{\circ}$

and for this $\theta$,$\sin$ and $\text{cosec}$ is Positive as they lie in 2 nd Quadrant

$\sin ^2\theta +\cos ^2\theta =1$

$\sin ^2\theta =1-(\frac{-3}{5})^2$

$\sin ^2\theta =1-\frac{9}{25}$

$\sin ^2\theta =\frac{16}{25}$

$\sin \theta =\frac{4}{5}$

$\therefore \text{cosec}\ \theta =\frac{5}{4}$