 # How to Prove the CAST Diagram

### To prove the CAST Diagram

On your SHARP EL535 calculator press . Then type in   .

For X_Start: type in 90 and .

For X_Step: type in 15 and .

Look at the answers between -90 and 0 – are they all positive or all negative?

They are all negative: therefore sin is negative between -90 and 0.

Between 0 and 90 sin is positive,

between 90 and 180 sin is ?

between 180 and 270 sin is ?

and between 270 and 360 sin is?

Press twice then type in  . Leave your X_Start and X_Step as they were for sin, so press twice. Again look at the ANS column and say between -90 and 0 whether cos is positive or negative; for 0 to 90, 90 to 180, 180 to 270 and 270 to360.

Repeat the process for tan.

Now write down all your information in a table:

sin cos tan who is
positive?
quadrant
-90 – 0 + cos 4
0 – 90 + + + all 1
90 – 180 + sin 2
180 – 270 + tan 3
270 – 360 + cos 4

Now we can summarise our results in a the form of a cartesian plane, where each quadrant represent the positive function: And that is where the the CAST diagram comes from. The line between C and A represents 0 or 360, the line between A and S represents 90, the line between S and T represents 180 and the line between T and C represents 270 or -90.