If `sintheta=3/5,tanphi=1/2 and pi/2ltthetaltpi phi<(3pi)/ 2` find the values of `8` `tan` `theta` `-``sqrt(5)` `sec ``phi`` < pi ``< phi<(3pi)>`

Explanation

We have:

`sin theta=frac{3}{5}, tan phi=frac{1}{2}` and `frac{pi}{2}
Thus, `theta` is in the second quadrant and `phi` is in the third quadrant. In the second quadrant, `cos theta` and `tan theta` are negative.

In the third quadrant, `sec phi` is negative.



`therefore cos theta=-sqrt{1-sin ^{2} theta}=-sqrt{1-left(frac{3}{5}right)^{2}}=frac{-4}{5}`

`tan theta=frac{3 / 5}{-4 / 5}=frac{-3}{4}`

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