CONTEXTUALIZED
LEARNING ACTIVITY
SHEET IN
PRECALCULUS
Subject Teacher:
Mrs. Jesabile Q. Adorable
Learner:
Daisy Mae C. Rulida
BASIC CONCEPTS OF UNIT CIRCLE
Lesson 1: UNIT CIRCLE
OBJECTIVES:
K: Identify the relationship between the linear and
angular measures of a central angle in a unit circle;
S: Illustrates the angles in standard position;
A: Appreciate the use of central angle in a unit circle to real-life situations.
Unit Circle
• Is the circle centered at the origin with radius 1. The equation of this circle is
x2 + y2 = 1 as shown below:
ANGLES IN STANDARD POSITION
An angel is formed by rotating a ray about its endpoint. It is said to be in
standard position if the vertex of the angle is at (0,0) and the initial side of the
angle lies along the positive x-axis. An angle measure is positive if the ray of
the angle rotates counterclockwise from the initial side to terminal side.
However, an angle measure is negative if the ray of the angle rotates
clockwise from the Initial side to terminal side.
Figure 1 is a positive angle since the rotation of the ray is Counterclockwise
while Figure 2 is a negative angle since the ray rotates Clockwise. Notice that
the terminal sides of Figure 1 and Figure 2 are in the Same position but they
do not represent the same angle (the direction of the Ray and the angle
measure are different). These angles are called coterminal.
Lesson 2:
CONVERTING ANGLES FROM DEGREE MEASURE TO RADIAN
MEASURE AND VICE VERSA
OBJECTIVES:
K: Define degree measure and radian measure;
S: Convert angle measure in degrees to radian and vice versa.
A: Develop appreciation in converting angle measure in degrees to radian and
vice versa.
The measure of an angle is determined by the amount of rotation from the
initial side to the terminal sides.
Measuring angles
One minute is one-sixtieth of a degree and denoted as 1’. One second is
one-sixtieth of a minute and is denoted by 1”.
Angles are also classified according to the quadrant in which their terminal
sides lie.
Example: Name the quadrant in which each angle lies.
A radian is the angle subtended at the center of a circle by an arc whose
length is equal to the radius of a circle.
A central angle (angle that forms when two radii meet at the center) of the
unit circle that intercepts an arc of the circle with length 1 unit is said to have a
measure of one radian, written 1 rad. As in the figure below,
RULES IN CONVERTING DEGREE TO RADIAN, and VICE VERSA
1. To convert a degree measure to radian, multiply it by 𝜋 𝑟𝑎𝑑 180
2. To convert a radian measure to degree, multiply it by 180𝜋 𝑟𝑎𝑑
The figure below shows some special angles in standard position with the
Indicated terminal sides. The degree and radian measures are also given.
Example. Express 75° and 240° in radians
Solutions:
Example . Express 𝜋/8 rad and 11𝜋/6 rad in degrees.
Solutions:
Activity 1. Identify the given angles as POSITIVE ANGLE or NEGATIVE
ANGLE.
Activity 2. Identify the terminal points of the given angle in standard position.
Activity 3. Sketch each of the following angles in standard position. (You may
use protractor for a better output).
1. Ѳ = 120˚
2. Ѳ = -45˚
3. Ѳ = -130˚
4. Ѳ = 45˚
5. Ѳ = 90˚
Activity 4. Identify the terminal side of an angle in standard position.
1. 135˚
2. -90˚
3. 405˚
Activity 5. Identify the terminal side of an angle in standard position.
Activity 6. Work with degree and radian measure. Use the conversion factor to
complete the solution.
Activity 7. Match column A with column B.
Activity 8. Identify the terminal side of an angle in standard position with given
measure.
Activity 9. Convert degree to minutes and seconds
1. 10.505°
2. 5.106°
Activity 10. Convert minutes and seconds to degrees
1. 10° 30’ 18”
2. 5° 6’ 21.6”
Answers key:
Activity 1.
1. Positive Angle
2. Negative Angle
3. Positive Angle
4. Positive Angle
5. Negative Angle
Activity 2.
Activity 3.
Activity 4.
Activity 5.
Activity 6.
Activity 7.
Activity 8.
Activity 9.
1. 10.505°
= 10 (.505 x 60)’
= 10 (30.3’)
= 10° 30.3’
= 10° 30’ (.3 x 60)”
= 10° 30’ 18”
2. 5.106°
= 5 (.106 x 60)’
= 5 (6.36’)
= 5° 6.36’
= 5° 6’ (.36 x 60)”
= 5° 6’ 21.6”
Activity 10.
1. 10° 30’ 18”
= 10° (30 + 18/60)
= 10° 30.3’
= (10° + 30.3/60)
= 10. 505°
2. 5° 6’ 21.6”
= 5° (6+ 21.6/60)
= 5° 6.36’
= (5°+ 6.36/60)
= 5.106°
