Question

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

Answer 1

Answer:
`(5)/(4)`

Explanation:

Given

`\cos \theta =(-3)/(5)`

and
`\theta` lies between

`90^(\circ)<\theta <180^(\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-((-3)/(5))^2`

`\sin ^2\theta =1-(9)/(25)`

`\sin ^2\theta =(16)/(25)`

`\sin \theta =(4)/(5)`

`\therefore \text{cosec}\ \theta =(5)/(4)`