Determine the slope of the straight line that makes a positive angle with the positive direction of the -axis, given that the sine of the positive angle is .
The slope, , of a straight line is equal to the tangent of the positive angle, , that the line makes with the positive direction
using the calculator, we get
This is a negative value and we require the positive angle.
The diagram shows that because the negative measure of the angle with the positive -axis is , then the positive measure of the angle is .
So, the slope of the line is the tangent of .