Since tan theta = 5/4 and cos theta < 0, we can use the trigonometric identities to find sin theta.
We know that
tan theta = sin theta / cos theta.
Given tan theta = 5/4, we can write
5/4 = sin theta / cos theta.
We also know that cos theta < 0, which means cos theta is negative.
Since we have a positive tangent value (5/4) and a negative cosine value, we can conclude that the sine value must be negative in the fourth quadrant.
Therefore, we can rewrite the equation as
-5/4 = sin theta / (- cos theta).
Simplifying further, we get
sin theta = -5/4 * (- cos theta) = 5/4 * cos theta.
Since we don't have the exact value for cos theta, we cannot find the exact value for sin theta. However, we can determine that sin theta is negative in the fourth quadrant.
Find the value of the sin theta function if tan theta = 5/4 and cos theta < 0
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