Find the value of secant theta for angle theta in standard position if a point with coordinates (-3/4) lies on its terminal side

Answer 1

When in STD position, the center i8s at
the origin:

C(h , k),
C(0 , o), P(-3 , 4),

r^2 = (x - h)^2 + (y - k)^2,
r^2 = (-3 - 0)^2 + (4 - 0)^2,
r^2 = 9 + 16 = 25,

r = 5.

rcos(theta) = x -h = -3 -0 = -3,
5cos(theta) = -3,
cos(theta) = -3/5 = -0.6,
theta = 126.9 deg.

Sec(theta) = 1/cos(theta) = 1/-0.6 =
-1.67.