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

Video Transcript

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

So we have this 𝑥, 𝑦-point. And if we were to plot this on a graph, 𝑥 is positive and 𝑦 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 that’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 let’s think about these 𝑥, 𝑦-coordinates for a minute. The 𝑥-coordinate of the point where the terminal side of an angle measuring 𝜃 in standard position which is what we have in a rectangular corner system intersects the unit circle is cos 𝜃, and the 𝑦-coordinate is sin 𝜃.

And since it’s asking for sin 𝜃, we know that it’s equal to negative four-fifths. Therefore, sin of 𝜃 is equal to negative four-fifths.