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A full rotation?
360 degrees or 2(pi) radians of angle.
Why is 90 degrees taken as angle of reference in trigonometry?
It is not. The angle of reference is 2*pi radians or 360 degrees.
What is the limit of arc tan?
The principal range of arc tan is an angle in the open interval (-pi/2, pi/2) radians = (-90, 90) degrees.
Why does the formula for area of a sector one half r-squared theta not hold true if theta is measured in degrees?
If this is a homework assignment, please consider trying it yourself first, otherwise the value of the reinforcement to the lesson offered by the homework will be lost on you.The area of a circle is pi r2.The area of a sector, defined as the proportion of an angle theta over the angle of a full circle is (pi r2 theta) / (2 pi). That simplifies to (r2 theta) / 2.Using degrees, the same equation is (pi r2 theta) / 360. That does not simplify any further.The reason for this is that theta in radians is defined as the proportion of the circumference of the circle, which is 2 pi r. This makes the math come out easier, which is why most trigonometry is done in radians, not degrees.
What is one fourth of a rotation going counterclockwise?
1/4 of 360 degrees = 90 degrees which is a right angle
