# If sin(theta)=-(13/15) and cos(theta) >0, find the exact value of tan ( theta)

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`sin(theta)=-13/15,and cos(theta)>0 => thetainIV` quadrant.

So will `tan(theta)<0.`

`Thus`

`cosec(theta)=-15/13`

`cosec^2(theta)-1=cot^2(theta)`

`cot^2(theta)=56/169`

`cot(theta)=+-sqrt(56/169)`

`But tan(theta)<0`

`therefore`

`cot(theta)<0`

`=> cot(theta)=-sqrt(56/169)`

`therefore`

`tan(theta)=-13/sqrt(56)`

The value of `sin theta = -(13/15)` .

Use the relation `sin^2theta + cos^2theta = 1` to determine `cos theta` .

`(-13/15)^2 + cos^2theta = 1`

`cos theta = sqrt(1 - 169/225)`

It is given that cos theta is greater than 0. Therefore` cos theta = (2*sqrt 14)/15`

`tan theta = (sin theta)/(cos theta)`

= `(-13/15)/((2*sqrt 14)/15)`

= `-13/(2*sqrt 14)`