Question

The terminal ray of ∠A passes through the point (−4,−6). ∠A is drawn in standard position. What is the value of cscA?

a) (-√13/6)
b) (-2√13/3)
c) (-√13/2)
d) (-3√13/2)

Answer 1

The terminal ray of ∠A passes through the point (−4,−6). ∠A is drawn in standard position. The value of csc(A) is -√13/6. Option A is answer.

Step-by-step explanation:

Locate the point: Since the terminal ray of angle A passes through (-4, -6), we know this point lies on the unit circle in standard position.

Calculate hypotenuse: Apply the Pythagorean theorem to find the hypotenuse of the right triangle formed by the x and y coordinates.

Hypotenuse = √(-4^2 + (-6)^2) = √(16 + 36) = √52 = 2√13.

Determine opposite: In standard position, the y-coordinate represents the opposite side for angles in Quadrant III. Therefore, the opposite side = -6.

Calculate csc(A): Recall that csc(A) = 1/sin(A) = opposite/hypotenuse. Substituting the values, we get csc(A) = -6/(2√13) = -3√13/13 = -√13/6.

Therefore, the value of csc(A) is -√13/6, corresponding to option a).