Trigonometric Conversions and Identities

This video tutorial explains how to convert between cylindrical and rectangular equations. It covers several examples, including converting y = 1, x = y^2, and z = x^2 + y^2 from rectangular to cylindrical form, and r = 2, r = 3 cos(θ), and θ = π/3 from cylindrical to rectangular form. The video emphasizes the importance of understanding the relationships between the variables and provides step-by-step solutions for each example.

What is the first step in converting a rectangular equation to cylindrical form?

• Replace x and y with r and theta

• Replace z with r and theta

• Replace r and theta with x and y

• Replace x and y with z

In the conversion of y = 1 to cylindrical form, what trigonometric identity is used?

• tangent

• sine

• cosine

• secant

When converting x = y^2 to cylindrical form, what is the expression for y^2 in terms of r and theta?

• r sin(theta)

• r cos(theta)

• r^2 cos^2(theta)

• r^2 sin^2(theta)

What is the cylindrical form of the equation z = x^2 + y^2?

• z = r

• z = r cos(theta)

• z = r^2

• z = r sin(theta)

In converting r = 2 to rectangular form, what is the resulting equation?

• x^2 + y^2 = 1

• x^2 + y^2 = 8

• x^2 + y^2 = 2

• x^2 + y^2 = 4

What is the rectangular form of r = 3 cos(theta)?

• x^2 + y^2 = 3x

• x^2 + y^2 = 9x

• x^2 + y^2 = 3y

• x^2 + y^2 = 9y

Why is it sometimes better to multiply by r instead of squaring both sides when converting to rectangular form?

• To make the equation linear

• To eliminate theta

• To simplify the equation

• To avoid complex trigonometric identities

What is the rectangular form of theta = pi/3?

• y = sqrt(3)x

• y = x/sqrt(3)

• y = x/3

• y = 3x

What trigonometric function is used to convert theta = pi/3 to rectangular form?

• Sine

• Cosine

• Tangent

• Cosecant

What is the value of tangent(pi/3) used in the conversion to rectangular form?

• 2

• 1/sqrt(3)

• sqrt(3)

• 1