Video Transcript
Find sin ๐, given ๐ is in standard position and its terminal side passes through the point three-fifths, negative four-fifths.
So we have this ๐ฅ, ๐ฆ-point. And if we were to plot this on a graph, ๐ฅ is positive and ๐ฆ is negative, so we would be in quadrant four. So again, we would be in quadrant four.
The quadrants start in the upper right-hand corner, and it goes counterclockwise. And it says that the terminal side passes through this point. So when we create an angle, we start at the initial side thatโs at zero degrees, and we keep going around counterclockwise until we get to our terminal side.
And it says this terminal side goes through the point three-fifths, negative four-fifths, so letโs think about these ๐ฅ, ๐ฆ-coordinates for a minute. The ๐ฅ-coordinate of the point where the terminal side of an angle measuring ๐ in standard position which is what we have in a rectangular corner system intersects the unit circle is cos ๐, and the ๐ฆ-coordinate is sin ๐.
And since itโs asking for sin ๐, we know that itโs equal to negative four-fifths. Therefore, sin of ๐ is equal to negative four-fifths.
