Answer:[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Given
[tex]\cos \theta =\frac{-3}{5}[/tex]
and [tex]\theta [/tex] lies between
[tex]90^{\circ}<\theta <180^{\circ}[/tex]
and for this [tex]\theta[/tex],[tex]\sin[/tex] and [tex]\text{cosec}[/tex] is Positive as they lie in 2 nd Quadrant
[tex]\sin ^2\theta +\cos ^2\theta =1[/tex]
[tex]\sin ^2\theta =1-(\frac{-3}{5})^2[/tex]
[tex]\sin ^2\theta =1-\frac{9}{25}[/tex]
[tex]\sin ^2\theta =\frac{16}{25}[/tex]
[tex]\sin \theta =\frac{4}{5}[/tex]
[tex]\therefore \text{cosec}\ \theta =\frac{5}{4}[/tex]
