Polar Coordinates and Angles

The video tutorial explains how to convert Cartesian coordinates (-4, -4) to polar coordinates (r, theta). It begins by plotting the point on a coordinate plane and sketching a reference triangle in the third quadrant. The tutorial then calculates the distance r using the Pythagorean theorem and determines the angle theta using the arctangent function. It highlights the importance of recognizing reference angles and using a calculator to verify results. The final polar coordinates are presented in both exact and decimal forms.

What is the interval for theta in polar coordinates?

• 0 to 2 pi radians

• -2 pi to 2 pi radians

• 0 to pi radians

• -pi to pi radians

Tags

CCSS.6.NS.C.6B

In which quadrant is the point (-4, -4) located?

• Third quadrant

• Second quadrant

• Fourth quadrant

• First quadrant

Tags

CCSS.HSN.CN.B.4

What is the formula for calculating r in polar coordinates?

• r = sqrt(x^2 + y^2)

• r = x^2 + y^2

• r = x + y

• r = sqrt(x + y)

What is the simplified form of the square root of 32?

• 16

• 4

• 4 sqrt(2)

• 8

Tags

CCSS.HSF.TF.A.2

What is the reference angle for theta when the tangent is 1?

• pi radians

• 3pi/4 radians

• pi/2 radians

• pi/4 radians

Tags

CCSS.HSF.TF.B.7

Why is the angle given by the calculator not the one we want in the third quadrant?

• Because the calculator only gives angles in the first quadrant

• Because the calculator gives a reference angle

• Because the calculator is in degree mode

• Because the calculator cannot calculate angles in the third quadrant

Tags

CCSS.HSF.TF.A.2

What is the exact angle theta in the third quadrant for the point (-4, -4)?

• 5pi/4 radians

• 3pi/4 radians

• 7pi/4 radians

• pi/4 radians

What is the decimal approximation of the angle theta in the third quadrant?

• 1.5708 radians

• 0.7854 radians

• 3.9270 radians

• 3.1416 radians

Tags

CCSS.HSN.CN.B.4

What are the polar coordinates for the Cartesian point (-4, -4)?

• 4, pi/4 radians

• 4 sqrt(2), 5pi/4 radians

• 4 sqrt(2), 3pi/4 radians

• 4, 7pi/4 radians

Tags

CCSS.HSN.CN.B.4

Which of the following is an acceptable approximation for the polar angle in the homework system?

• 3.9270 radians

• 3.1416 radians

• 1.5708 radians

• 0.7854 radians

Tags

CCSS.HSN.CN.B.4