Question

For the following equations find 1) the general form for all solutions 2) the solutions on the interval (pi/2)<=θ<3pi in terms of pi. cscθ=2

Answer 1

Explanation:

`\csc( \alpha ) = 2`

We know that

`\csc( \alpha ) = (1)/( \sin( \alpha ) )`

So

`\sin( \alpha ) = (1)/(2)`

Our general solutions are

`(\pi)/(6) + 2\pi(k)`

where. k is a integer ,

and

`(5\pi)/(6) + 2\pi(k)`

where k is an integer

2. Using our general solutions,

the only answers that lies between the suggested regions are

`(5\pi)/(6)`

`(13\pi)/(6)`

`(17\pi)/(6)`