### Video Transcript

Find the tangent of ๐, given ๐ is in standard position and its terminal side passes through the point negative three-fifths, negative four-fifths.

Since this is an ๐ฅ-๐ฆ point, letโs think about where this will be located. In quadrant number one, ๐ฅ and ๐ฆ would be positive. In quadrant two, ๐ฅ would be negative and ๐ฆ would be positive. And in quadrant three thatโs in the bottom left-hand corner, ๐ฅ would be negative and ๐ฆ would be negative. And in the fourth quadrant, ๐ฅ would be positive and ๐ฆ would be negative.

So since ๐ฅ and ๐ฆ are both negative, we will be in quadrant three, because weโre in the negative direction for ๐ฅ and in the negative direction for ๐ฆ. When we create an angle, thereโs an initial side and a terminal side. The terminal side is when it stops, so weโre gonna stop in quadrant three. And it says that this terminal side passes through the point negative three-fifths, negative four-fifths.

The ๐ฅ-coordinate of the point where the terminal side of an angle measuring ๐ in standard position in a rectangular coordinate system intersects the unit circle is cos ๐, and the ๐ฆ-coordinate is sin ๐. Since the angle is in standard position and its terminal side intersects the unit circle at a point with the coordinate of negative three-fifths, negative four-fifths, sin of ๐ must be equal to negative four-fifths and cos of ๐ must be equal to negative three-fifths.

Now tangent of ๐ will be equal to the sin of ๐ divided by the cos of ๐, so we have negative four-fifths divided by negative three-fifths. And when we divide fractions, we actually multiply by the reciprocal, so we keep our negative four-fifths, but instead of dividing by the denominator, we multiply by the denominatorโs reciprocal, so we flip it.

And now we multiply. The fives cancel and the two negatives cancel to become a positive, so we get four-thirds. Therefore, the tangent of ๐ is equal to four-thirds.