Angle A appears in 2 triangles: ABC and ANC, where N is the point where the perpendicular from C meets AB.
In terms of sides we can write:
sinA=BC/AB=CN/AN; cosA=AN/AC=AC/AB; tanA=BC/AC=CN/AN.
Now put in some numbers (AN=9, AB=12):
sinA=BC/12=CN/9; cosA=9/AC=AC/12; tanA=BC/AC=CN/9.
We can see that 9/AC=AC/12, so AC^2=108 and AC=√108=6√3. Therefore cosA=6√3/12=√3/2.
sinA=√(1-(cosA)^2)=√(1-3/4)=1/2; tanA=sinA/cosA=1/2*2/√3=1/√3=√3/3.
cosecA=1/sinA=2; secA=1/cosA=2/√3=2√3/3; cotA=1/tanA=√3.
Respectively to 4 decimal places these are:
cosA=0.8660; sinA=0.5000; tanA=0.5774; secA=1.1547; cosecA=2.0000; cotA=1.7321.