Sorry ok I was talking about on the unit circle how come the slope of the reference line (say if you were to angle pi/2, the reference line would be the positive y axis from y equals zero to y equals one, I think this line is called this, like if you were to draw pi/4 on the unit circle you would indicate this by drawing a line that is not on the circle arleady... this line is the line I'm referencing) how come the slope of this line or the first deriviative of it is equal to tangent

Question

Sorry ok I was talking about on the unit circle how come the slope of the reference line (say if you were to angle pi/2, the reference line would be the positive y axis from y equals zero to y equals one, I think this line is called this, like if you were to draw pi/4 on the unit circle you would indicate this by drawing a line that is not on the circle arleady... this line is the line I'm referencing)  how come the slope of this line or the first deriviative  of it is equal to tangent

tan theta = (dsine(theta))/(dcos(theta))

???

Joe · Answer

tangent theta is equal to the derivative of sine theta over the derivative of cosine theta?

bobpursley · Answer

I think you are greatly confused.

The slope of any line at an angle theta from the reference line is equal to tangent theta.

tangenttheta is NOT equal to derivative of sin over the derivative of cosine.

Why is slope equal to tangent?

slope is defined as deltaY/deltax where x is the reference point for the angle. but deltaY/deltaX is by definition the tangent of the central angle, theta.