How to use the power reduction formulas to derive the half-angle formulas.
How to use the sine and cosine addition formulas to prove the double-angle formulas.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
Understanding the half-life of a radioactive substance.
How to define a tangent line; how to determine the angle a radius to a tangent forms.
How to use half reactions to understand oxidation-reduction.
How to derive two more cosine double-angle formulas.
How to evaluate the tangent of 3*pi/4.
How to define the tangent function for all angles.
Understanding the differences between empirical and molecular formulas.
How to find the angle of inclination of a line.
How to define an angle of elevation or an angle of depression.