The unit circle and the functions sine, cosine, tangent

In Year 2 we had met the sine and cosine as ratios between the sides of a right-angled triangle, defined only for acute angles. In Year 4 we make a qualitative leap: we turn the sine and cosine into genuine functions of a real variable, defined for any angle, even negative or greater than a full turn. The key object is the unit circle, the circle of radius $1$ centred at the origin. The chapter introduces the measurement of angles in radians, defines $\sin,\cos,\tan$ as the coordinates of a point on the circle, studies their notable values, periodicity, graphs and associated arcs, presents the inverse functions $\arcsin,\arccos,\arctan$ and closes with polar coordinates, a second language for describing the points of the plane.

Sezioni

• Angles in radians
• The unit circle
• Definition of sine, cosine, tangent
• Notable values
• Periodicity
• Graphs of the trigonometric functions
• Associated arcs
• Inverse functions: arcsin, arccos, arctan
• Polar coordinates in the plane

Esercizi

• All the worked exercises of the chapter