all triangles are taken to exist in euclidean geometry, so that the inside angles of each triangle sum to π radians (or 180°); therefore, for a right triangle, the two non-right angles are between zero and π/2 radians. notice that strictly speaking, the following definitions only define the trigonometric functions for angles in this range. we extend them to the full set of real arguments by using the unit circle, or by requiring certain symmetries and that they be periodic functions.