Question

the point p(x, y) lies on the terminal side of an angle θ = -60° in standard position. what are the signs of the values of x and y? both x and y are positive. both x and y are negative. x is positive, and y is negative. x is negative, and y is positive.

Explanation:

Step1: Determine the quadrant of \(\theta = -60^\circ\)

An angle of \(-60^\circ\) in standard position is measured clockwise from the positive \(x\)-axis. This angle is equivalent to \(360^\circ - 60^\circ = 300^\circ\) (measured counterclockwise), which lies in the fourth quadrant.

Step2: Recall the sign conventions for coordinates in each quadrant

In the fourth quadrant, the \(x\)-coordinate (abscissa) is positive, and the \(y\)-coordinate (ordinate) is negative. So for a point \(P(x, y)\) on the terminal side of \(\theta = -60^\circ\), \(x\) is positive and \(y\) is negative.

Answer:

x is positive, and y is negative. (The option corresponding to this description, e.g., if it's the third option in the list, state the option with its text as per the original problem's options layout)