Question

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?

Answer 1

To find sin(theta) for a point in Quadrant IV with a given x-coordinate on the unit circle, we need to find the y-coordinate using the equation y = sqrt(1 - x^2). Then, we can calculate sin(theta) using the equation sin(theta) = y/r, where r is the radius of the unit circle.

sin(theta) = -56/65

Step-by-step explanation:

To find sin(theta), we first need to determine the value of y. Since P is in Quadrant IV, the y-coordinate will be negative. The y-coordinate can be found using the equation y = sqrt(1 - x^2). Plugging in x = 33/65, we get y = sqrt(1 - (33/65)^2). Evaluating this expression, we find y = -56/65.

Now that we have the values of x and y, we can find sin(theta) using the equation sin(theta) = y/r, where r is the radius of the unit circle which is 1. Plugging in the values, we have sin(theta) = (-56/65)/1 = -56/65.

Answer 2

cos theta = adj / hyp = (33/65) / 1 = 33/65
sin^2 theta = 1 = cos^2 theta = 1 - (33/65)^2 = 3136/4225
sin theta = sqrt(3136 / 4225) = 56/65

Therefore, sin theta = -56/65 (4th quadrant)