Mastering Reference Angles and Quadrants in Radians

A clock shows the time as 3:00. What is the reference angle in radians for the angle formed by the hour and minute hands?

• 2.3562

• 0.7854

• 3.1416

• 1.5708

An angle of 150 degrees is in which quadrant? What is its reference angle in radians?

• Fourth quadrant, reference angle: π/2 radians

• Third quadrant, reference angle: π/4 radians

• First quadrant, reference angle: π/3 radians

• Second quadrant, reference angle: π/6 radians

A skateboarder performs a trick that requires them to rotate 240 degrees. What is the reference angle in radians and which quadrant does it lie in?

• 4π/3 radians, second quadrant

• 5π/3 radians, fourth quadrant

• 2π/3 radians, third quadrant

• π/3 radians, first quadrant

A Ferris wheel rotates 300 degrees from the starting point. What is the reference angle in radians and which quadrant does it fall into?

• 3π/4 radians, Third quadrant

• 2π/3 radians, Fourth quadrant

• π/3 radians, First quadrant

• 5π/6 radians, Second quadrant

A soccer player kicks the ball at an angle of 135 degrees. Determine the reference angle in radians and identify the quadrant.

• 2π/3 radians, Third quadrant

• π/3 radians, First quadrant

• π/6 radians, Fourth quadrant

• π/4 radians, Second quadrant

A cyclist travels in a circular path and turns 225 degrees. What is the reference angle in radians and which quadrant is this angle located in?

• π/3 radians, first quadrant

• π/4 radians, third quadrant

• 3π/4 radians, fourth quadrant

• π/2 radians, second quadrant

An artist paints a mural that includes an angle of 330 degrees. What is the reference angle in radians and which quadrant does it belong to?

• π/3 radians, first quadrant

• 5π/6 radians, third quadrant

• π/6 radians, fourth quadrant

• π/4 radians, second quadrant

A drone is flying at an angle of 120 degrees. What is the reference angle in radians and which quadrant is it in?

• π/3 radians, Second Quadrant

• 2π/3 radians, Fourth Quadrant

• π/2 radians, Third Quadrant

• π/4 radians, First Quadrant

A diver enters the water at an angle of 45 degrees. What is the reference angle in radians and which quadrant does it lie in?

• Reference angle: π/3 radians; Quadrant: Second quadrant

• Reference angle: π/4 radians; Quadrant: First quadrant

• Reference angle: π/6 radians; Quadrant: Fourth quadrant

• Reference angle: π/2 radians; Quadrant: Third quadrant

A wind turbine rotates 150 degrees. What is the reference angle in radians and which quadrant does this angle occupy?

• Reference angle: π/4 radians, Quadrant: I

• Reference angle: π/2 radians, Quadrant: IV

• Reference angle: π/6 radians, Quadrant: II

• Reference angle: π/3 radians, Quadrant: III