Understanding the Unit Circle

This video tutorial by Mr. Bourne covers the unit circle, explaining its properties, the concept of radians, and their relationship with degrees. It provides formulas for converting between degrees and radians and demonstrates how to find exact XY coordinates of important radian measures on the unit circle. The tutorial is designed to be concise, covering all topics in under 8 minutes.

What is the radius of a unit circle?

• π

• 0.5

• 2

• 1

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How many radians are there in a full circle?

• 2π

• 3π

• 4π

• π

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What is the degree equivalent of one radian?

• 180°

• 90°

• 57°

• 45°

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Which of the following is equivalent to 90° in radians?

• π/4

• π/2

• π

• 2π

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What is the formula to convert degrees to radians?

• degrees * π / 180

• degrees / 180 * π

• degrees * 180 / π

• degrees / π * 180

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If you have 1.5 radians, how many degrees is that approximately?

• 95.5°

• 90°

• 100°

• 85.9°

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What are the coordinates for 30° on the unit circle?

• (1/2, √3/2)

• (√3/2, 1/2)

• (1, 0)

• (0, 1)

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Which trigonometric function gives the y-coordinate on the unit circle?

• Tangent

• Cotangent

• Sine

• Cosine

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What is the x-coordinate for 60° on the unit circle?

• 1/2

• 1

• √3/2

• 0

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Which of the following is a strategy for memorizing unit circle coordinates?

• Use random numbers

• Memorize all decimals

• Look for symmetry

• Ignore negative signs

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