Finding a trig value, like trig(A):
Remember: In this type of problem, A is a distance around the unit circle, and we are trying to find some value associated with the terminal point.
1. Find the reference number for A.
2. Find the terminal point for the reference number.
3. Find or calculate the appropriate trig value for the terminal point.
4. Adjust the plus/minus sign on the trig value, depending on the quadrant for A.
Example: Find sin(11π/3):
1. The reference number for 11π/3 is π/3. (Remember: As long as the fraction 11π/3 is reduced, you simply change the numerator to 1π, so you get 1π/3, or π/3.)
2. The terminal point for π/3 is (1/2, sqrt(3)/2).
3. Since our trig function is sine, and the sine is the y-value of the terminal point, our trig value is sqrt(3)/2.
4. Counting around the unit circle, we find that 11π/3 is in the 4th quadrant. Since sine is negative in the 4th quadrant, we put a minus sign on our trig value: Our answer is -sqrt(3)/2.
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