Should the unit circle be committed to memory for the DAT?
There's no need to memorize the entire unit circle. Here's an easy way to know in which quadrant is the angle located;
First you need to know the basic angles in the first quadrant: π/6 π/4 π/3 and know their sine cosine etc...
If any other angle is given look at the numerator and denominator.
If the the numerator is less than the denominator by 1 you're in the 2nd quadrant.
For example: 2π/3. 3π/4. 5π/6. 7π/8. Etc....
If the numerator is greater than the denominator by 1 you're in 3rd quadrant.
For example: 5π/4. 7π/6. 4π/3. 11π/10. Etc.....
If the numerator is greater than the denominator by more than 1 you're in the 4th quadrant.
For example: 5π/3. 7π/4. 8π/5. Etc....
Be careful with the last case. If the angle is more than 2π that will bring you back to other quadrants.
For example 7π/3 will bring you back to the first quadrant.
In a case like this just subtract 2π.
7π/3 - 2π = π/3. Which is in the first quadrant.
Hope this helps..