Chapter 5 Trigonometric Functions

Trigonometry connects angles, lengths, coordinates, and periodic change. Water Engineering Technology applications include surveying, pipe slopes, tank geometry, channel measurements, rotating equipment, and seasonal or cyclic signals. This chapter follows the MATH 128 notes from angle measure and right triangles through special angles, reference angles, the unit circle, trigonometric graphs, transformations, inverse functions, and identities. Exact values are retained when they clarify structure, while decimal approximations are used when a measured length or angle is required.

Learning outcomes. By the end of this chapter, you should be able to:

• convert angles between degrees and radians and identify coterminal angles;
• solve right triangles using trigonometric ratios;
• evaluate trigonometric functions using reference angles and the unit circle;
• state domains and graph sine, cosine, and tangent functions;
• model periodic behaviour with transformed sine and cosine functions;
• use inverse trigonometric functions to determine angles; and
• verify identities and apply fundamental angle formulas.