Exploring Polar Coordinates in the Second Quadrant

Professor Anderson explains polar coordinates using a problem involving x = -3 and y = 4. The video covers the calculation of r and theta, using trigonometric relations and the properties of a 3-4-5 right triangle. The process involves determining the hypotenuse and using cosine to find the angle theta, which is then used to calculate the polar angle.

What are the x and y coordinates given in the example?

• x = 3, y = -4

• x = -4, y = 3

• x = -3, y = 4

• x = 4, y = -3

In which quadrant does the point (-3, 4) lie?

• Quadrant IV

• Quadrant I

• Quadrant II

• Quadrant III

What is the formula to calculate r in polar coordinates?

• r = sqrt(x^2 + y^2)

• r = x^2 + y^2

• r = sqrt(x^2 - y^2)

• r = x + y

What is the value of r for the coordinates (-3, 4)?

• 5

• 7

• 3

• 4

What type of triangle is formed by the coordinates (-3, 4) in the context of r?

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

• Right triangle

What is the hypotenuse of the triangle formed by the coordinates (-3, 4)?

• 3 units

• 4 units

• 5 units

• 6 units

Which trigonometric function is used to calculate phi in this example?

• Sine

• Cosine

• Tangent

• Cotangent

What is the value of phi when calculated using cosine?

• 37 degrees

• 45 degrees

• 127 degrees

• 53 degrees

What is the correct expression for theta in terms of phi?

• Theta = 180 + phi

• Theta = 180 - phi

• Theta = phi - 180

• Theta = phi + 180

What is the value of theta for the given coordinates?

• 127 degrees

• 53 degrees

• 180 degrees

• 37 degrees