Understanding Angles in Standard Position and Coterminal Angles

This video tutorial introduces angles in standard position, explaining how to plot them and determine coterminal angles. It covers the concept of quadrantal angles and provides examples of coterminal angles, such as 30, 390, and -330 degrees. The tutorial demonstrates how to find coterminal angles for given angles, including both positive and negative measures, and provides expressions to express all angles coterminal to a specific angle. The video aims to enhance understanding of angle rotation and coterminal angles in geometry.

What is the defining characteristic of an angle in standard position?

• It is always a right angle.

• Its vertex is at the origin and the initial side is on the positive x-axis.

• It is always greater than 180 degrees.

• It is always less than 90 degrees.

In which quadrant does an angle between 90 and 180 degrees lie?

• Fourth Quadrant

• Third Quadrant

• Second Quadrant

• First Quadrant

What is a quadrantal angle?

• An angle whose terminal side lies on one of the axes.

• An angle that is greater than 360 degrees.

• An angle that is less than 0 degrees.

• An angle that lies in the first quadrant.

Which of the following angles is coterminal with 30 degrees?

• 60 degrees

• 120 degrees

• -60 degrees

• 390 degrees

How can you find a positive coterminal angle for 135 degrees?

• Add 360 degrees

• Subtract 90 degrees

• Subtract 360 degrees

• Add 90 degrees

If an angle is 495 degrees, what is its coterminal angle between 0 and 360 degrees?

• 225 degrees

• 135 degrees

• 315 degrees

• 45 degrees

What is the least positive coterminal angle for -65 degrees?

• 65 degrees

• 295 degrees

• -295 degrees

• 360 degrees

What is the coterminal angle of 1070 degrees with the least positive measure?

• 350 degrees

• 360 degrees

• 720 degrees

• 10 degrees

What is the coterminal angle of -225 degrees with the least positive measure?

• 135 degrees

• 225 degrees

• 315 degrees

• 45 degrees

How do you express all angles coterminal to 90 degrees?

• 90 + 90n, where n is an integer

• 90 + 270n, where n is an integer

• 90 + 360n, where n is an integer

• 90 + 180n, where n is an integer