Identifying Unit Circle Coordinates

00:00 4 marks

Consider the unit circle. Answer the following:

(a) List the coordinates for the angles 0°, 90°, 180°, and 270° on the unit circle.

(b) Explain how negative angles are interpreted on the unit circle and determine the coordinates for an angle of -30°.

Part a

3 minutes 2 marks

Question

List the coordinates on the unit circle for the angles 0°, 90°, 180°, and 270°.

Hint Hint

Hint

Recall that the coordinate for 0° is (1,0) and use symmetry for other angles.

Answer Answer
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Answer Answer

Complete Answer

0°: (1, 0), 90°: (0, 1), 180°: (-1, 0), 270°: (0, -1)

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Part b

2 minutes 2 marks

Question

Explain how negative angles are interpreted on the unit circle and determine the coordinates for an angle of -30°.

Hint Hint

Hint

Remember that negative angles represent clockwise rotation from the positive x-axis.

Answer Answer
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Answer Answer

Complete Answer

An angle of -30° is a clockwise rotation of 30° from the positive x-axis. Its coordinates are \(\left(\cos(-30°), \sin(-30°)\right) = \left(\cos(30°), -\sin(30°)\right)\), which simplifies to \(\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)\).

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