Hello, dagbayani481!

$\displaystyle \tan \theta = \text{-}4 ,\;\;\sin \theta > 0$

$\displaystyle \text}Find all of the trignometric values of }\theta.$

We know that tangent is negative in quadrants 2 and 4.

We know that sine is positive in quadrants 1 and 2.

. . Hence, $\displaystyle \,\theta$ is in quadrant 2.

Code:

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We know that: .$\displaystyle \tan\theta \:=\:-\dfrac{4}{1} \:=\:\dfrac{opp}{adj}$

So the diagram looks like this:

Code:

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-1

We have: .$\displaystyle opp = 4,\;adj = \text{-}1$

Pythagorus says: .$\displaystyle hyp \:=\:\sqrt{4^2 + (\text{-}1)^2} \:=\:\sqrt{17}$

Now you can write all six trigonometric values.