Let x = 33/65 be the x-coordinate of the point P(x,y), where the terminal side of angle theta (in standard position) meets the unit circle. If P is in Quadrant IV, what is sin(theta)?
In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. Since the x-coordinate is 33/65, we can find the y-coordinate using the Pythagorean theorem.
Let y = -sqrt(1 - (33/65)^2).
Therefore, sin(theta) = y = -sqrt(1 - (33/65)^2).
To simplify further, we can express 1 - (33/65)^2 as a common denominator:
1 - (33/65)^2 = (65^2 - 33^2) / 65^2
= (65 + 33)(65 - 33) / 65^2
= (98)(32) / 65^2
= (112)(8) / 65^2.
Finally, sin(theta) = -sqrt(112/65^2) = -sqrt(112)/65.
Therefore, sin(theta) is -sqrt(112)/65.