if `theta` is an angle in standard position and its terminal side passes through the point (-3, 2) , find the exact value of csc`theta` ?

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If the terminal side of the angle passes through the point (-3,2), the angle is in the second quadrant (Q2).

theta is the angle which is made by the line and positive direction of x. Therfore theta is an obtuse angle.

According to the graph,

`sin(pi-theta) = 2/sqrt(2^2+3^2)`

`=...

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If the terminal side of the angle passes through the point (-3,2), the angle is in the second quadrant (Q2).

theta is the angle which is made by the line and positive direction of x. Therfore theta is an obtuse angle.

According to the graph,

`sin(pi-theta) = 2/sqrt(2^2+3^2)`

                  `= 2/sqrt(13)`

But we know, `sin(pi-theta)=sin(theta)`

Therefore `sin(theta) = 2/sqrt(13)`

`cosec(theta) = 1/sin(theta) = 1/(2/sqrt(13))`

 

Therefore the answer is `cosec(theta) = sqrt(13)/2`

 

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