Inequality

Suppose that there are three points A,B and C on a line where C is between A and B. o is any other point not on the line. Prove that OA+OB>OC

Prove that adjacent angles around a point and covering an entire plane add up to 360

Prove (using angle,ray,line,plane axioms)That the sum of the measures of any set of adjacent angles about a point, whose sides and interiors cover the entire plane is 360. I was attempting to do this with the definition of supplimentary angles. What I can't get past though is how I can convert the half-planes into angles measuring 180 when you can have a set of angles with any measurements. No portion of the set may add up to 180. Can you help me at least get started?

Find the shaded area (see figure)

Imagine a valley y=x^2. A circle with radius = 5 is inside it. Another circle, with radius = 4 is above the previous circle, (and inclined to right side) (PLEASE SEE THE ATTACHMENT zip file) Find the area between y=x^2 and the 2 circles (not allow to use computer)

Trigonomic Points in terms of Radians

In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle) 1) A reflection y = x followed by a rotation through pi 2) A reflection in y = -x 3) A reflection in the x axis followed by a rotation in the y axis 4) A rotation through -pi / 2 followed by a reflection in the y axis. In each case, give the corresponding related angle formulas involving cos & sin.

Trigonometric Points in Terms of Radians

Complete the attached table using exact notation. For the column p(X) this is the co-ordinates that are needed for that particular point. Hope that this is clear!!