Reference Angles and Trig

What is the reference angle for 41π/45 radians?

• -4π/45 radians

• 4π/45 radians

• 49π/45 radians

• 37π/90 radians

Answer explanation

Since 0.5 < 41/45 < 1, this is a 2nd quadrant angle. This means the reference angle is π - 41π/45 = 45π/45 - 41π/45 = 4π/45.

What is the reference angle for 5π/9 radians?

• 4π/9 radians

• -4π/9 radians

• 13π/9 radians

• π/18 radians

Answer explanation

Since 0.5 < 5/9 < 1, this is a 2nd quadrant angle. This means the reference angle is π - 5π/9 = 9π/9 - 5π/9 = 4π/9.

What is the reference angle for 17π/30 radians?

• 13π/30 radians

• -13π/30 radians

• 43π/30 radians

• π/15 radians

Answer explanation

Since 0.5 < 17/30 < 1, this is a 2nd quadrant angle. This means the reference angle is π - 17π/30 = 30π/30 - 17π/30 = 13π/30.

What is the reference angle for 38π/15 radians?

• -7π/15 radians

• 7π/15 radians

• 22π/15 radians

• π/30 radians

Answer explanation

This angle is bigger than 2π, so we need to subtract 2π to get a coterminal angle (38π/15 - 30π/15 = 8π/15). This is a 2nd quadrant angle, so the reference angle is π - 8π/15 = 15π/15 - 8π/15 = 7π/15.

What is the reference angle for 19π/18 radians?

• -π/18 radians

• 17π/18 radians

• 4π/9 radians

• π/18 radians

Answer explanation

Note that 1 < 19/18 < 1.5, so this is a 3rd quadrant angle. This means the reference angle is 19π/18 - π = 19π/18 - 18π/18 = π/18.

What is the reference angle for 7π/6 radians?

• -π/6 radians

• 5π/6 radians

• π/3 radians

• π/6 radians

Answer explanation

Note that 1 < 7/6 < 1.5, so this is a 3rd quadrant angle. This means the reference angle is 7π/6 - π = 7π/6 - 6π/6 = π/6.

What is the reference angle for 6π/5 radians?

• -π/5 radians

• 4π/5 radians

• 3π/10 radians

• π/5 radians

Answer explanation

Note that 1 < 6/5 < 1.5, so this is a 3rd quadrant angle. This means the reference angle is 6π/5 - π = 6π/5 - 5π/5 = π/5.

What is the reference angle for 47π/30 radians?

• 13π/30 radians

• -13π/30 radians

• 17π/30 radians

• π/15 radians

Answer explanation

Note that 1.5 < 47/30 < 2, so this is a 4th quadrant angle. This means the reference angle is 2π - 47π/30 = 60π/30 - 47π/30 = 13π/30.

What is the reference angle for 26π/15 radians?

• 11π/15 radians

• -4π/15 radians

• 4π/15 radians

• 7π/30 radians

Answer explanation

Note that 1.5 < 26/15 < 2, so this is a 4th quadrant angle. This means the reference angle is 2π - 26π/15 = 30π/15 - 26π/15 = 4π/15.

What is the reference angle for 11π/6 radians?

• -π/6 radians

• 5π/6 radians

• π/6 radians

• π/3 radians

Answer explanation

Note that 1.5 < 11/6 < 2, so this is a 4th quadrant angle. This means the reference angle is 2π - 11π/6 = 12π/6 - 11π/6 = π/6.