The method using a clinometer goes one step further than the earlier method in that it translates the proportional reasoning in the triangles into the trigonometric function
In spite of these strange properties, we can define a measure of angles and trigonometric functions
that have apparently similar properties than common trigonometric functions
of Euclidean geometry.
For example, n = 3 for trigonometric function
(Problems 13 in Table IV) and n = 2 for the Rosenbrock function (Problem 14) of Algorithm 566.
Li, "A sharp double inequality for trigonometric functions
and its applications," Abstract and Applied Analysis, vol.
Huybrechs in  proposed a new set of trigonometric functions
, which includes sines and cosines as well as half-sines and half-cosines.
The model was estimated using the set of trigonometric functions
defined by (15) for D = 4.
Quinlan (2004) and Cavanagh (2008) engaged students with hands-on activities involving tangent ratios before formally introducing trigonometric functions
. As echoed by Bressoud (2010), Weber (2005) introduced circle trigonometry before triangle trigonometry.
To derive relations between joint variables [[theta].sub.1], [[theta].sub.2], [[theta].sub.3] and the coordinates [[x.sub.E], [y.sub.E]] of the end-effector we simply apply definitions of trigonometric functions
sine and cosine (see Figure 9)
As applications of Theorem 3 in engineering problems, we present several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions
in this section.
As it integrates the concepts of trigonometric functions
and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.
Exploration 6.1: Trigonometric Functions
. After rigorously developing the mapping properties of the sine function, we would ask the students to conjecture about the mapping properties of the cosine function, and then test the conjecture immediately.
Transmission functions could be expressed by polynomial functions or by trigonometric functions
(Simionescu et al., 1996).