Unit Circle Concepts and Properties

The video tutorial introduces analytic geometry as a blend of algebra and geometry. It explains the unit circle and its equation, demonstrating how to prove the Pythagorean identity using the unit circle. The tutorial covers the relationship between trigonometric functions and the unit circle, providing a specific example to verify the identity. The lesson emphasizes understanding geometric shapes through algebraic equations and the application of trigonometric identities.

What is the main idea behind analytic geometry?

• It combines algebra and geometry.

• It is a branch of calculus.

• It combines algebra and calculus.

• It focuses solely on geometric shapes.

What is the radius of the unit circle?

• 0

• 1

• 3

• 2

On the unit circle, what does the x-coordinate represent?

• Cotangent of theta

• Sine of theta

• Tangent of theta

• Cosine of theta

What is the equation of the unit circle?

• x^2 + y^2 = 0

• x^2 + y^2 = 1

• x^2 + y^2 = 2

• x^2 + y^2 = 3

How can any point on the unit circle be labeled?

• As (secant theta, cosecant theta)

• As (tangent theta, cotangent theta)

• As (cosine theta, sine theta)

• As (sine theta, cosine theta)

What identity is proven using the unit circle?

• Sine squared theta plus cosine squared theta equals one

• Sine squared theta plus cosine squared theta equals three

• Sine squared theta plus cosine squared theta equals zero

• Sine squared theta plus cosine squared theta equals two

Which quadrant has both x and y as negative on the unit circle?

• Third quadrant

• First quadrant

• Second quadrant

• Fourth quadrant

What is the sine of 180 degrees on the unit circle?

• 0.5

• -1

• 0

• 1

What is the cosine of 180 degrees on the unit circle?

• 1

• 0

• -1

• 0.5

What does the Pythagorean identity confirm for the point (-1, 0) on the unit circle?

• It satisfies the identity.

• It only satisfies the identity for negative angles.

• It does not satisfy the identity.

• It only satisfies the identity for positive angles.