What is a reference angle of 240?
A 240-degree angle is between 180 and 270 degrees, so its terminal side is in QIII. Do the operation indicated for that quadrant. Subtract 180 from 240. You find that 240 – 180 = 60, so the reference angle is 60 degrees.
Can a reference angle be over 90 degrees?
The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.
What is the reference angle for 333?
Precalculus Examples The resulting angle of 333° 333 ° is positive and coterminal with −27° – 27 ° . Since the angle 333° is in the fourth quadrant, subtract 333° from 360° .
What is the reference angle of a negative angle?
Negative angles (strictly between 0∘ and −180∘ ) put you in quadrants III and IV. For example, −23∘ is in quadrant IV, and its reference angle is 23∘ .
Why do Quadrantal angles not have reference angles?
Quadrantal Angles: Angles 0°, 90°, 180°, 270°, and 360° do not have reference angles because they are quadrantal angles.
What is the symbol for a reference angle?
Figure %: In each drawing, β is the reference angle for θ. For example, sin( ) = ±sin( ). We know this because the angle is the reference angle for . Because we know that the sine function is negative in the third quadrant, we know the whole answer: sin( ) = – sin( ).
What is the reference angle for an angle of?
Rules for Reference Angles in Each Quadrant
|Quadrant||Angle, θ||Reference Angle Formula in Radians|
|I||lies between 0° and 90°||θ|
|II||lies between 90° and 180°||π – θ|
|III||lies between 180° and 270°||θ – π|
|IV||lies between 270° and 360°||2π – θ|