# PracticeReference Angle

#### puremath

##### New member
Find the reference angle or reference number.

NOTE: WHAT IS THE DIFFERENCE BETWEEN A REFERENCE ANGLE AND REFERENCE NUMBER?

A. 60°

B. -60°

C. 5pi/4

#### MarkFL

##### La Villa Strangiato
Math Helper
The reference angle is the smallest angle subtended by a radius $$0\le\theta\le\dfrac{\pi}{2}$$ and the $$x$$-axis, and the reference number is the shortest distance along the unit circle to the $$x$$-axis. Since the radius of the unit circle is by definition 1 unit, the reference number and reference angle (if given in radians) will have the same value.

A. Let's make a diagram:

We can see the reference angle is $$60^{\circ}$$ and the reference number is $$\dfrac{\pi}{3}$$, which we get by converting the reference angle to radians.

#### puremath

##### New member
The reference angle is the smallest angle subtended by a radius $$0\le\theta\le\dfrac{\pi}{2}$$ and the $$x$$-axis, and the reference number is the shortest distance along the unit circle to the $$x$$-axis. Since the radius of the unit circle is by definition 1 unit, the reference number and reference angle (if given in radians) will have the same value.

A. Let's make a diagram:

View attachment 1447

We can see the reference angle is $$60^{\circ}$$ and the reference number is $$\dfrac{\pi}{3}$$, which we get by converting the reference angle to radians.

Is there an algebraic method?

#### puremath

##### New member
The reference angle is the smallest angle subtended by a radius $$0\le\theta\le\dfrac{\pi}{2}$$ and the $$x$$-axis, and the reference number is the shortest distance along the unit circle to the $$x$$-axis. Since the radius of the unit circle is by definition 1 unit, the reference number and reference angle (if given in radians) will have the same value.

A. Let's make a diagram:

View attachment 1447

We can see the reference angle is $$60^{\circ}$$ and the reference number is $$\dfrac{\pi}{3}$$, which we get by converting the reference angle to radians.