Reference Angles

Drawing Angles in Standard Position

Quadrants

Finding Reference angle by Quadrant

• Quadrant 1 - itself

• Quadrant 2 - 180 Degrees minus the angle

• Quadrant 3 - The angle minus 180 degrees

• Quadrant 4 - 360 minus the angle

Finding Reference Angles

• The blue portion of graph is the original angle

• The red portion is reference angle

  
  

Coterminal Angles

On slide 6, angles 500° and 140° are coterminal because their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of 360°.

Ex: Find one Positive and one Negative Angle that are coterminal with -45° and 395°

​There are many such angles, depending on what multiple of 360° is added or subtracted.

Multiple Choice

Which of the following angles are co-terminal to 330^o?

• -330^o, 330^o

• 510^o, -210^o

• 690^o, -30^o

• 420^o, -330^o

Multiple Choice

Which of the following angles are co-terminal to -75^o?

• -365^o, 75^o

• 285^o, -435^o

• 105^o, -255^o

• 425^o, -335^o

Multiple Choice

Which of the following angles are co-terminal to -35^o?

• 325^o, -395^o

• 395^o, -325^o

• 145^o, -215^o

• -125^o, 325^o

Multiple Choice

Which quadrant is -570⁰. Keep adding 360 until the number is positive.

• I

• II

• III

• IV

Multiple Choice

What is the reference angle?

• 43

• -43

• 47

• -47

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the reference angle for -30°?

• 150°

• 30°

• 80°

• 60°

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°