Understanding Reference Angles and Quadrants

The video tutorial explains how to find the reference angle and the smallest possible positive angle for a point on the terminal side of an angle in the coordinate plane. It begins by plotting the point (-8, 3) in the second quadrant and discusses the properties of angles and their reference angles. The tutorial then calculates the tangent and inverse tangent to find the reference angle, ensuring the calculator is in radian mode. It concludes by determining the smallest positive angle using the reference angle and provides a final calculation of approximately 2.7828 radians.

In which quadrant is the point (-8, 3) located?

• Quadrant IV

• Quadrant I

• Quadrant III

• Quadrant II

What is the initial side of an angle on the coordinate plane?

• Along the positive y-axis

• Along the negative x-axis

• Along the negative y-axis

• Along the positive x-axis

What is the formula for tangent of an angle in the coordinate plane?

• y divided by x

• x plus y

• x minus y

• x divided by y

What is the reference angle for the point (-8, 3)?

• 0.3588 radians

• 3.3588 radians

• 1.3588 radians

• 2.3588 radians

What is the significance of ensuring the calculator is in radian mode?

• To get the angle in degrees

• To get the angle in radians

• To get the angle in gradians

• To get the angle in revolutions

What is the inverse tangent of -3/8 approximately equal to?

• 0.3588

• -1.3588

• -0.3588

• 1.3588

Why does the angle in the fourth quadrant have the same tangent value as the angle in the second quadrant?

• x is positive and y is negative in both quadrants

• x and y have opposite signs in these quadrants

• x is negative and y is positive in both quadrants

• Both x and y are positive in both quadrants

What is the relationship between the reference angle and the angle in the second quadrant?

• The reference angle is the complement of the angle

• The reference angle is twice the angle

• They are equal

• The reference angle is half the angle

How do you calculate the smallest positive angle using the reference angle?

• Add the reference angle to pi

• Divide pi by the reference angle

• Subtract the reference angle from pi

• Multiply the reference angle by pi

What is the smallest positive angle in radians for the point (-8, 3)?

• 4.7828 radians

• 3.7828 radians

• 2.7828 radians

• 1.7828 radians