Final answer:
Trigonometry is the mathematical study focused on the relationships between the angles and sides of triangles, using ratios such as sine, cosine, and tangent, along with identities like the Law of Sines and the Law of Cosines to solve problems.
Step-by-step explanation:
The subject matter of trigonometry deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. Trigonometry has practical applications in many fields including engineering, physics, and astronomy. Central to understanding trigonometry are the trigonometric ratios, which are sine (sin), cosine (cos), and tangent (tan). These functions are important as they allow for the determination of unknown angles and sides of triangles given certain known sides or angles.
Trigonometric identities, like the Law of Sines and the Law of Cosines, are essential tools for solving problems involving triangles. The Law of Sines relates side lengths of a triangle to the sines of its angles, while the Law of Cosines allows us to find the sides and angles of a triangle when we know other sides and angles.
Example Problems
Various trigonometric problems may involve the use of these identities and ratios. Challenge problems and exercises like those mentioned (e.g., sin 20, cos 20, etc.) require an application of these principles to solve for unknown variables in specific trigonometric equations or scenarios.