# Geometric Interpretation

The trigonometric functions are defined from the orthogonal triangular as a ratio of its sides. In order to interpret them geometrically we will use the unit circle. The unit circle consists of a circle of radius length of one unit, which is set on the centre of the Cartesian coordinates. We will also consider a line of angle θ in respect to axis x, that begins from the origins of the Cartesian system and intersects the unit circle at the point A.

In image 1 we can see how sine, cosine and tangent are geometrically interpreted. Sine is the length of the y axis from its origin up to the projection of the point A on the y axis, cosine is the length of the x axis from its origin up to the projection of the point A on the x axis and tangent is the length of the tangent of the unit circle at the point A, from that point, up to the point that it intersects the axis x.

**Image 1: Sine, Cosine, Tangent**

In image 2 we can see how secant, cosecant and cotangent are geometrically interpreted. Secant is the length of the x axis from its origin up to the point where the tangent of point A intersects the x axis. Cosecant is the length of the y axis from its origin up to the point where the tangent of point A intersects the y axis. Cotangent is the length of the tangent of point A, from this point, up to the point that it intersects the y axis.

**Image 2: Secant, Cosecant, Cotangent**

Angle θ can vary around the unit circle. This is why the graphs repeat themselves every 360 degrees.