Question

19. If theta is an angle in standard position and its terminal

side passes through the point (-2,1), find the exact value of
csc(theta) in simplest radical form.

Answer 1

To find the exact value of csc(theta) in simplest radical form, we first need to determine the coordinates of the point on the terminal side of the angle in standard position.

Since the terminal side passes through the point (-2,1), we know that the point is on the line y = 1. To find the exact value of csc(theta), we need to find the distance between the point (-2,1) and the origin (0,0). This distance is given by the expression sqrt((-2)^2 + 1^2) = sqrt(5).

Therefore, csc(theta) = 1/sin(theta) = 1/sqrt(5)

Explanation: