교과서 질문
Find the reference angle for each angle.
-25π/6
703
views
3. Unit Circle
Reference Angles
객관식
Which set of ordered pairs represents angles in standard position that share the same reference angle?
A
and
B
and
C
and
D
and
검증된 단계별 안내1
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.
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.
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.
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.
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.
관련 영상
관련 실천
