Which set of ordered pairs represents angles in standard position that share the same reference angle?

• A. $(2,3)$ and $(-2,-3)$
• B. $(-3,2)$ and $(3,-2)$
• C. $(4,5)$ and $(-4,5)$
• D. $(1,0)$ and $(0,1)$

Answer: (C)

Verified step by step guidance

1. Step 1: Understand that angles in standard position are measured from the positive x-axis, and their coordinates on the unit circle correspond to (cos \theta, sin \theta). The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.
2. Step 2: Recognize that two angles share the same reference angle if their terminal sides form the same acute angle with the x-axis, even if they lie in different quadrants. This means their sine and cosine values have the same absolute values but may differ in sign depending on the quadrant.
3. Step 3: For each pair of ordered pairs (x, y), interpret them as coordinates corresponding to (cos \theta, sin \theta) for some angle \theta. Compare the absolute values of the x and y components in each pair to check if they match, indicating the same reference angle.
4. Step 4: Identify the pair where the x-coordinates have the same absolute value and the y-coordinates have the same absolute value, but the signs differ appropriately to place the points in different quadrants. This confirms they share the same reference angle.
5. Step 5: Conclude that the correct pair is the one where the coordinates differ only by the sign of the x-component (or y-component) but have the same absolute values, representing angles with the same reference angle in different quadrants.