Final answer:
The question lacks specific arguments for the trigonometric functions. Trigonometric identities like the sum to product identities could be used to solve such expressions if more information were provided. Relevant identities include the Law of Sines and Law of Cosines.
Step-by-step explanation:
The student is asking to find the exact value of an expression involving the sine, cosine, and inverse tangent functions. However, the question seems to be incomplete or may have typos, as it's written simply as 'sin(cos()-tan-1())', which lacks specific arguments for the functions. To provide a clear answer, more information or clarification is needed from the student. If we had specific values for cos() and tan-1(), we could provide the exact value by first finding the angle given by the inverse tangent (tan-1), then finding the cosine of that angle, and finally the sine of the result.
Consider the trigonometric identities provided, such as the sin and cos formulas for double angles (í13. and 14.), and the sum to product identities (í15. and 16.), which show relationships between different trigonometric functions. The information about antinodes in a wave equation and conservation of momentum are not directly relevant to solving a trigonometric expression.
Based on the identities given, if we have an angle value or can determine one from a tangent value, we use trigonometric identities to find the precise sine or cosine values. For example, Law of Sines and Law of Cosines could be used in the context of triangles to find missing angles or sides when given sufficient information.