What are the pythagorean identities

The video tutorial introduces the Pythagorean theorem in the context of right triangles and extends this concept to trigonometric functions using the unit circle. It explains how sine, cosine, and tangent relate to the unit circle and derives Pythagorean identities. The tutorial emphasizes the importance of these identities in simplifying equations and solving problems, providing a foundation for further study in trigonometry.

What is the significance of the unit circle in relation to the Pythagorean theorem?

• It is unrelated to trigonometry.

• It helps in calculating the area of a circle.

• It provides a visual representation of trigonometric functions.

• It is used to measure angles in degrees.

How is the sine of an angle represented in the unit circle?

• As the radius of the circle.

• As the x-coordinate of the point on the circle.

• As the y-coordinate of the point on the circle.

• As the angle in radians.

Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right triangle?

• Sine

• Cosine

• Tangent

• Secant

What does the Pythagorean identity 'sine squared plus cosine squared equals one' imply?

• It is irrelevant to trigonometric functions.

• It is only applicable to isosceles triangles.

• It is used to calculate the hypotenuse of a triangle.

• It is a fundamental relationship in trigonometry.

Which of the following is a Pythagorean identity?

• 1 + sine squared = cosine squared

• 1 + tangent squared = secant squared

• 1 + cosine squared = sine squared

• 1 + cotangent squared = tangent squared