A few examples of what you can ask Wolfram|Alpha about:
Trigonometric Calculations
compute values of trigonometric functions
compute values of inverse trigonometric functions
Trigonometric Functions
compute properties of a trigonometric function
compute properties of an inverse trigonometric function
plot a trigonometric function
analyze a trigonometric function of a complex variable
analyze a trigonometric polynomial
generate a table of special values of a function
compute the root mean square of a periodic function
Trigonometric Identities
find multiple-angle formulas
find addition formulas
find other trig identities
Trigonometric Equations
solve a trigonometric equation
Trigonometric Theorems
apply a trigonometric theorem
apply the Pythagorean theorem
Spherical Trigonometry
apply a theorem of spherical trigonometry