Practice Reference 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:

tml_0021.png


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.

 
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