Aims

To provide necessary knowledge in basic trigonometry

and train skills to use trigonometry fluently in

various circumstances.

Content

Angles and their measure. The unit circle. Trigonometric

functions: sine, cosine, tangent, cotangent,

secant, cosekant.

Trigonometric formulas: complementary angles, addition formulas,

double angle and half-angle formulas. Mnemonic rules to memorize

formulas.

Trigonometry in triangles. Trigonometry in geometry.

Simplification of trigonometric expressions.

Expressing all

trigonometric functions as functions of a

tangent of half angle.

Rational parametrisation of a circle. Pythagorean triples.

Diophantine equations.

The complex exponential. Euler's formulas.

Inverse trigonometric functions: arcsine, arccosine, arctangent.

Trigonometric equations and inequalities.

Hyperbolic functions. Inverse hyperbolic functions.

Instruction

Lectures and problem solving sessions.

Assessment

Quizzes.