# Question Video: Finding the Value of a Trigonometric Function of an Angle given the Coordinates of the Point of Intersection of the Terminal Side and the Unit Circle Mathematics • 10th Grade

Find sin ๐, given ๐ is in standard position and its terminal side passes through the point (3/5, โ4/5).

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### 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 ๐ฅ, ๐ฆ-point. And if we were to plot this on a graph, ๐ฅ is positive and ๐ฆ 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 thatโs 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 letโs think about these ๐ฅ, ๐ฆ-coordinates for a minute. The ๐ฅ-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 ๐ฆ-coordinate is sin ๐.

And since itโs asking for sin ๐, we know that itโs equal to negative four-fifths. Therefore, sin of ๐ is equal to negative four-fifths.