Exploring the Unit Circle Concepts

What is the radius of the unit circle?

• 0

• 1

• 2

• 0.5

What does the radian measure represent in the context of the unit circle?

• The area of the circle

• The circumference of the circle

• The ratio of arc length to radius

• The diameter of the circle

What are the coordinates of the critical points on the unit circle?

• (1,0), (0,1), (-1,0), (0,-1)

• (1,1), (0,0), (-1,-1), (0,0)

• (2,0), (0,2), (-2,0), (0,-2)

• (0.5,0), (0,0.5), (-0.5,0), (0,-0.5)

In a 45-45-90 triangle, what is the length of the side opposite the 45-degree angle?

• Square root of 2 over 2

• Square root of 2

• 1

• 1 over square root of 2

How is the hypotenuse of a 45-45-90 triangle related to its legs in the unit circle?

• Equal to the length of one leg

• Square root of 2 times the length of each leg

• Half the length of each leg

• Twice the length of each leg

What is the length of side 'b' in a 30-60-90 triangle when the hypotenuse is 1?

• Square root of 3 over 2

• 0.5

• 1

• 2

Which side length is directly across from the 60-degree angle in a 30-60-90 triangle?

• b over 2

• b

• 2b

• b times square root of 3

What are the coordinates of the point representing 30 degrees on the unit circle?

• (1/2, square root 3 over 2)

• (1, 0)

• (0, 1)

• (square root 3 over 2, 1/2)

What is the sine of 30 degrees?

• 1/2

• square root 3 over 2

• square root 2 over 2

• 1

In which quadrant does an angle of 135 degrees lie?

• First

• Fourth

• Second

• Third