Skip to main content
Logo image

Precalculus for Team-Based Inquiry Learning: PREVIEW Edition — Instructor Version

TBIL Community

Section 6.1 Degree and Radian Measure (TR1)

Subsection 6.1.1 Activities

Definition 6.1.1.

anglevertex

Activity 6.1.2.

We know that if you complete a full turn of the circle the angle created will be 360 degrees. Use this to estimate the measure of the given angles.
(a)
Figure 6.1.3.
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 135^{\circ}\)
  4. \(\displaystyle 180^{\circ}\)
Answer.
B
(b)
Figure 6.1.4.
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 135^{\circ}\)
  4. \(\displaystyle 180^{\circ}\)
Answer.
D
(c)
Figure 6.1.5.
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 135^{\circ}\)
  4. \(\displaystyle 180^{\circ}\)
Answer.
C

Definition 6.1.6.

An angle is in standard position if its vertex is located at the origin and its initial side extends along the positive \(x\)-axis.
Figure 6.1.7.
An angle measured counterclockwise from the initial side has a positive measure, while an angle measured clockwise from the initial side has a negative measure.
Figure 6.1.8.

Activity 6.1.9.

Find the measure of the angles drawn in standard position.
(a)
Figure 6.1.10.
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 135^{\circ}\)
  4. \(\displaystyle 180^{\circ}\)
Answer.
A
(b)
Figure 6.1.11.
  1. \(\displaystyle 180^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle -180^{\circ}\)
  4. \(\displaystyle -90^{\circ}\)
Answer.
C
(c)
Figure 6.1.12.
  1. \(\displaystyle 30^{\circ}\)
  2. \(\displaystyle -150^{\circ}\)
  3. \(\displaystyle -210^{\circ}\)
  4. \(\displaystyle 210^{\circ}\)
Answer.
D
(d)
Draw an angle of measure \(-225^{\circ} \) in standard position.
Answer.
Figure 6.1.13.

Remark 6.1.14.

\(C=2\pi r\)\(360^{\circ}=2\pi\)

Definition 6.1.15.

One radian is the measure of a central angle of a circle that intersects an arc the same length as the radius.

Activity 6.1.16.

Using the fact that one turn around the circle is \(360^{\circ}\) and also \(2\pi\) radians. Find the measure of the following angles in radians.
(a)
\(180^{\circ}\)
  1. \(\displaystyle \frac{\pi}{4}\)
  2. \(\displaystyle \pi\)
  3. \(\displaystyle \frac{3\pi}{4}\)
  4. \(\displaystyle \frac{\pi}{2}\)
Answer.
B
(b)
\(45^{\circ}\)
  1. \(\displaystyle \frac{\pi}{4}\)
  2. \(\displaystyle \pi\)
  3. \(\displaystyle \frac{3\pi}{4}\)
  4. \(\displaystyle \frac{\pi}{2}\)
Answer.
A

Activity 6.1.17.

Using the fact that one turn around the circle is \(360^{\circ}\) and also \(2\pi\) radians. Find the measure of the following angles in degrees.
(a)
\(\frac{\pi}{2}\)
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 180^{\circ}\)
  4. \(\displaystyle 360^{\circ}\)
Answer.
B
(b)
\(\frac{3\pi}{4}\)
  1. \(\displaystyle 45^{\circ}\)
  2. \(\displaystyle 90^{\circ}\)
  3. \(\displaystyle 135^{\circ}\)
  4. \(\displaystyle 180^{\circ}\)
Answer.
C

Exercises 6.1.2 Exercises

PrevTopNext