Learn to basics of eliminating the parameter with sine and cosine

The video tutorial explains how to eliminate the parameter in parametric equations to derive the standard equation of a circle. It begins by discussing the relationship between cosine, sine, and parametric equations of a circle. The instructor then introduces the geometric form and Pythagorean identity, showing how to express cosine and sine in terms of x and y. Finally, the tutorial demonstrates converting these expressions into the standard equation of a circle, x^2 + y^2 = r^2, with a specific example where the radius is 5.

What does the equation x squared plus y squared equals r squared represent in geometry?

• A parabola

• A circle

• A hyperbola

• An ellipse

Which identity is represented by cosine squared of t plus sine squared of t equals 1?

• Trigonometric Identity

• Euler's Identity

• Geometric Identity

• Pythagorean Identity

How can cosine of t be expressed in terms of x when the parameter is eliminated?

• 5 over y

• 5 over x

• y over 5

• x over 5

What is the resulting equation when the parametric form is converted to standard form?

• x squared plus y squared equals 1

• x squared plus y squared equals 5

• x squared plus y squared equals 25

• x squared plus y squared equals 10

What is the radius of the circle represented by the equation x squared plus y squared equals 25?

• 3

• 5

• 6

• 4