Trigonometry

Trigonometry studies the relationships between angles and side lengths in triangles, especially right triangles, using trigonometric ratios. The main trigonometric ratios are sine ($ext{sin}$), cosine ($ext{cos}$), and tangent ($ext{tan}$). For a right triangle with angle $A$, opposite side $a$, adjacent side $b$, and hypotenuse $c$, we define:

Important properties

• The Pythagorean identity: $\sin^2 A + \cos^2 A = 1$

• Trigonometric ratios depend only on the angle, not the size of the triangle

• Trigonometric functions are periodic and repeat their values in regular intervals