Radian Angle Measures on the Unit Circle

Being careful to not match colors, but radians for letters a (210 degrees), b (225 degrees), and c (240 degrees) - what matching best completes Quadrant II of the Unit Circle with Radian Measures?

• a

• 
• c

• 
• b

• 

Being careful to not match colors, but radians for letters a (300 degrees), b (315 degrees), and c (330 degrees) - what matching best completes Quadrant VI of the Unit Circle with Radian Measures?

• b

• 
• a

• 
• c

• 

Answer explanation

Thank you.

Please be prepared for additional unit circle questions on the next test and also throughout the rest of maths in your lives, as it is a vital concept.

Match the following vocabulary related to the Unit Circle

• Pythagorean Identity

• the ratio of the arc length formed by an angle divided by the r of that circle

• arc length

• measure of a central angle of a circle that intercepts an arc = in length to the r of that circle

• radian measure

• the length of the curve formed by an arc

• quadrantal angle

• states that the square of the cosine of a given angle + the square of the sine of that angle = 1

• radian

• an angle whose terminal sides lies on an axis

Now, for Quadrant I of the Unit Circle, please complete the coordinates before we move onto finish Degrees to Radians. Recall the importance of Desmos. Recall the importance of thinking in terms of two number lines intersecting at, "(0, 0)."

b

a

c

In the context of a Unit Circle:

What is the approximate most accurate simplification of 0.866, one-half [either the y or x half; (x, y)] of a coordinate pair in a cartesian Unit Circle representation, which of course does not reach a Unit Square point like, "(1, 1),"

• 
• 
• 
• 

• 1

• 2

• 0

Find an angle coterminal with an angle which measures 11π ∕ 3.

• 17 π / 3

• 4π ∕ 3

• π ∕ 3

• 8π ∕ 3

Find an angle coterminal with an angle measuring 17π / 4 radians.

• π ∕ 3

• 5π ∕ 4

• π ∕ 4

• 13π ∕ 4

Find the arc length indicated by the bolded arc. 

• 8.3 in

• 7.2 in

• 6.8 in

• 6.4 in

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

• 3 radian

• 2 radian

• 4 radian

• 2π radian