Unit Circle Concepts and Identities

The video reviews the unit circle definition of trigonometric functions, explaining how sine and cosine are derived from the x and y coordinates of a point on the unit circle. It introduces the Pythagorean identity, showing its derivation from the unit circle equation and its usefulness in calculating trigonometric functions. The video also clarifies why this identity is named after the Pythagorean theorem.

What is the radius of a unit circle?

• 1

• 0

• 3

• 2

Which point on the unit circle corresponds to the coordinates (0, 1)?

• Top

• Bottom

• Right

• Left

In the unit circle, what does the x-coordinate of a point represent?

• Sine of the angle

• Cosine of the angle

• Cotangent of the angle

• Tangent of the angle

What is the y-coordinate of a point on the unit circle called?

• Tangent of the angle

• Cosine of the angle

• Secant of the angle

• Sine of the angle

What is the equation of a unit circle centered at the origin?

• x^2 + y^2 = 3

• x^2 + y^2 = 0

• x^2 + y^2 = 1

• x^2 + y^2 = 2

What identity is derived from the unit circle equation?

• Pythagorean identity

• Geometric identity

• Trigonometric identity

• Algebraic identity

How can the Pythagorean identity help in finding tangent of an angle?

• By using sine and cosine

• By using secant and cosecant

• By using sine and cosecant

• By using cotangent and tangent

What is the relationship between the hypotenuse of a right triangle and the unit circle?

• Hypotenuse is always 3

• Hypotenuse is always 0

• Hypotenuse is always 1

• Hypotenuse is always 2

Why is the Pythagorean identity useful?

• It helps in finding angles

• It helps in finding trigonometric functions

• It helps in finding coordinates

• It helps in finding distances

What theorem is used to derive the equation of a circle?

• Pythagorean theorem

• Euclid's theorem

• Thales' theorem

• Fermat's theorem