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Coordinates on the Unit Circle Based upon the unit circle activity, we have found that the (x, y) coordinates on the unit circle match to the cos and sin of the angle. This means that if we know the coordinates of any angle on the unit circle, we could find sin, cos, and tan of that angle. Example: Given that the terminal side of an angle, π, crosses the UNIT CIRCLE at the point β 5 1 , 3 3 , what is the sin π, cos π, and tan π? Since the point is on the UNIT CIRCLE, the (x,y) matches to (cos π, sin π). sin π = cos π = To find the tan π, we can use what we know about SOH-CAH-TOA. Example conβt: Given that the terminal side of an angle, π, crosses the UNIT CIRCLE at the point β 5 1 , 3 3 , what is the sin π, cos π, and tan π? Another way you can find tan π is by a special relationship, π¬π’π§ π½ πππ§ π½ = . ππ¨π¬ π½ This means if you divide the value of sin by the value of cos, you will get the value of tan. Sin ÷ Cos keep, change, flip But what if the point is NOT on the unit circle? The (x, y) no longer represents the cos and sin of the angle. We can still use what we observed in the activity to help usβ¦ Any circle can represent the angles of rotation. If a coordinate lies on the terminal side of any angle, then those values are the horizontal and vertical sides of a right triangle. Example: The point (-3, 4) lies on the terminal side of an angle in standard position. This means that we have a triangle with a horizontal side of -3 and a vertical side of 4. Letβs draw this triangle and see if we can find the values of the 3 basic trigonometric functions. Letβs try anotherβ¦ The point (-2, -5) lies on the terminal side of an angle (π). Find the values of the 3 basic trigonometric functions.