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Given the point on the unit circle $\left( -\frac{3}{5}, -\frac{4}{5} \right)$, we need to determine the angle $\theta$ in radians.

First, note that the x and y coordinates tell us which quadrant the angle is in. Both coordinates are negative, so the point lies in the third quadrant.

The reference angle $\alpha$ can be determined using the tangent function:

$ \tan \alpha = \left| \frac{y}{x} \right| = \left| \frac{-\frac{4}{5}}{-\frac{3}{5}} \right| = \frac{4}{3} $

Using the arctangent function, we find:

$ \alpha = \arctan \left( \frac{4}{3} \right) $

Since this is a third quadrant angle, $\theta$ is given by:

$ \theta = \pi + \alpha $

Thus,

$ \theta = \pi + \arctan \left( \frac{4}{3} \right) $

Given the point $left( -frac{3}{5}, -frac{4}{5}
ight)$ on the unit circle, we need to find the angle $ heta$ in radians.

First, identify the quadrant. Both coordinates are negative, indicating the third quadrant.

The reference angle $alpha$ is determined by:

$ an alpha = left| frac{y}{x}
ight| = left| frac{-frac{4}{5}}{-frac{3}{5}}
ight| = frac{4}{3} $

Thus,

$ alpha = arctan left( frac{4}{3}
ight) $

Since the point is in the third quadrant:

$ heta = pi + alpha $

Substitute the value of $alpha$:

$ heta = pi + arctan left( frac{4}{3}
ight) $

For the point $left( -frac{3}{5}, -frac{4}{5}
ight)$ on the unit circle, identify the angle $ heta$ in radians.

Third quadrant identification leads to:

$ an alpha = frac{4}{3} $

So:

$ alpha = arctan left( frac{4}{3}
ight) $

Thus:

$ heta = pi + alpha = pi + arctan left( frac{4}{3}
ight) $

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