what is the sec x ratio for
a) sin(theta)=-1/2
To determine the sec x ratio, we first need to find the value of cos x, which is the reciprocal of sec x.
Given that sin(theta) = -1/2, we can use the Pythagorean Identity to find cos(theta):
sin^2(theta) + cos^2(theta) = 1
(-1/2)^2 + cos^2(theta) = 1
1/4 + cos^2(theta) = 1
cos^2(theta) = 1 - 1/4
cos^2(theta) = 3/4
Taking the square root of both sides:
cos(theta) = ± sqrt(3)/2
The value of cos(theta) can be positive or negative depending on the quadrant of the angle theta. However, we only need the positive value of cos(theta) to calculate the sec x ratio.
Since sec(theta) = 1/cos(theta), we have:
sec(theta) = 1/(sqrt(3)/2)
sec(theta) = 2/sqrt(3)
sec(theta) = (2 * sqrt(3))/3
Therefore, the sec x ratio for sin(theta) = -1/2 is (2 * sqrt(3))/3.