The angles which lie between 0º and 90º are said to lie in the first quadrant. The angles between 90º and 180º are in the second quadrant, angles between 180º and 270º are in the third quadrant and angles between 270º and 360º are in the fourth quadrant:

In the first quadrant, the values for sin, cos and tan are positive.
In the second quadrant, the values for sin are positive only.
In the third quadrant, the values for tan are positive only.
In the fourth quadrant, the values for cos are positive only.

This can be summed up as follows:

In the fourth quadrant, Cos is positive, in the first, All are positive, in the second, Sin is positive and in the fourth quadrant, Tan is positive. This is easy to remember, since it spells 'cast'.

 

Related angles
The sines, cosines and tangents of some angles are equal to the sines, cosines and tangents of other angles. For example, cos(-30º) = cos(30º) and cos(30º) = cos(390º) . In the following diagrams, the sines, cosines and tangents of each of the shaded angles have the same magnitude (ø is the same angle in each diagram):

 

 

Arcsin, arccos, arctan
Arcsin is another way of writing the inverse of sin, arccos means the inverse of cos and arctan means the inverse of tan. For example, arcsin(0.5) = 30º . However, although this is true, we also know that sin(150º) = 0.5 (using the idea of related angles and the 'cast rule'). If we continue moving round the 'unit circle' (the circle with radius 1 that we have been drawing angles on above), then we find that sin(390º) is also 0.5 .
So we can write arcsin(0.5) = 30º, 150º, 390º, ...

Solving Equations
Example:
Solve the equation sinø = 0.6428, for 0 < ø < 360º

therefore ø = arcsin(0.6428)
= 40º, 140º, 400º, ...
but the question asks for solutions between 0 and 360º, so the answer is 40º and 140º .

Graphing sinø, cosø and tanø
The following are graphs of sinø, cosø and tanø: