Find the vaule of sec(theta) for angle theta in standard position if the point at (3,-1) lies on its terminal side.
To find the value of sec(theta), we can use the relationship between sec(theta) and the coordinates of a point on the terminal side of the angle in standard position.
Let's start by plotting the point (3, -1) on the coordinate plane. The x-coordinate represents the value of cosine, and the y-coordinate represents the value of sine. Since the point is in quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.
The value of cosine(theta) is given by the x-coordinate divided by the radius of the unit circle, which is 1. So, cosine(theta) = 3/1 = 3.
Since sec(theta) is the reciprocal of cosine(theta), sec(theta) = 1/cosine(theta). Therefore, sec(theta) = 1/3.
The value of sec(theta) for the given angle is 1/3.
the radius is √[3^2 + (-1)^2] = √10
sec(Θ) = √10 / 3