Finding the function values on the unit circle is done by using reference angles. That last example 4π/3 is simple. All π/3 (60°) angles have a sine of √3/2 and a cosine of 1/2 and the the signs of those values are determined by the quadrant in which the angle lies. Since π/3 =180°/3 =60°. So we know this angle forms a 60° angle from the x-axis, and now you merely need to know in which quadrant it lies. It is π/3 past π or 3π/3. So, it is the Quadrant III, 60° angle. So both it sine and cosine values are negative. We know that 60° angles are taller than they are wider so, the function value that is great in magnitude is the sine value while rhe cosine value is 1/2.
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Thank you SO MUCH! You explained this so thoroughly in a way it was easy to understand.
You're very welcome!
Finding the function values on the unit circle is done by using reference angles. That last example 4π/3 is simple. All π/3 (60°) angles have a sine of √3/2 and a cosine of 1/2 and the the signs of those values are determined by the quadrant in which the angle lies.
Since π/3 =180°/3 =60°. So we know this angle forms a 60° angle from the x-axis, and now you merely need to know in which quadrant it lies. It is π/3 past π or 3π/3. So, it is the Quadrant III, 60° angle. So both it sine and cosine values are negative. We know that 60° angles are taller than they are wider so, the function value that is great in magnitude is the sine value while rhe cosine value is 1/2.