Understanding the relationship of polar and rectangular coordinates

The video tutorial explains the relationship between coordinates and distance in trigonometry, focusing on the unit circle where the radius (r) is 1. It covers the definitions of sine, cosine, and tangent, and how these are simplified on the unit circle. The tutorial also discusses the impact of different values of r on polar coordinates and emphasizes the importance of key trigonometric formulas.

What is the significance of 'r' in the context of trigonometry?

• It is the base of a triangle.

• It is the hypotenuse of a right triangle.

• It is the distance from the origin to a point.

• It represents the angle in a triangle.

How does the unit circle simplify the understanding of trigonometric functions?

• By setting the radius to 1, simplifying calculations.

• By making all sides of the triangle equal.

• By making all angles equal to 90 degrees.

• By eliminating the need for coordinates.

When r equals 1, what does the cosine of theta represent on the unit circle?

• The hypotenuse of the triangle.

• The angle theta itself.

• The x-coordinate of the point.

• The y-coordinate of the point.

How do you calculate x when r is not equal to 1 in polar coordinates?

• x equals r divided by the cosine of theta.

• x equals r times the sine of theta.

• x equals r times the cosine of theta.

• x equals r divided by the sine of theta.

What is the relationship between x, y, and r in trigonometry?

• x squared plus y squared equals r squared.

• x plus y equals r.

• x times y equals r squared.

• x divided by y equals r.