Trigonometric Coordinates in Quadrants

The video tutorial explains how to find exact coordinates on the unit circle for specific angles: 30°, 45°, and 60°. It covers how these coordinates can be determined using the Pythagorean theorem and how they apply across different quadrants. The tutorial also highlights the symmetry of the unit circle and how coordinates change signs depending on the quadrant.

What are the key angles in the first quadrant of the unit circle?

• 60°, 75°, 90°

• 30°, 45°, 60°

• 15°, 30°, 45°

• 45°, 60°, 75°

How do the coordinates change when moving from the first to the second quadrant?

• Both coordinates remain positive.

• Both coordinates become negative.

• The y-coordinate becomes negative.

• The x-coordinate becomes negative.

What is the x-coordinate of the 30° angle in the first quadrant?

• √2/2

• √3/2

• 1/2

• 1

In the third quadrant, what happens to the y-coordinate of the 30° angle?

• It doubles.

• It remains the same.

• It becomes positive.

• It becomes negative.

What is the coordinate of the 45° angle in the first quadrant?

• (√2/2, √2/2)

• (1, 0)

• (1/2, √3/2)

• (√3/2, 1/2)

How does the x-coordinate of the 45° angle change in the second quadrant?

• It doubles.

• It becomes positive.

• It becomes negative.

• It remains the same.

What is the y-coordinate of the 60° angle in the first quadrant?

• √2/2

• √3/2

• 1

• 1/2

In the fourth quadrant, what happens to the y-coordinate of the 60° angle?

• It becomes positive.

• It remains the same.

• It becomes negative.

• It doubles.

Which triangle shares the same x-coordinate as the 60° triangle in the first quadrant?

• None

• 30° triangle

• 45° triangle

• 60° triangle

What is the relationship between the 30° and 60° triangles in terms of their coordinates?

• They have the same y-coordinate.

• Their coordinates are flipped.

• They have the same coordinates.

• They have different coordinates.