ANGLES IN STANDARD
POSITION & COTERMINAL
ANGLES
OBJECTIVES
At the end of the lesson, the students
should be able to:
Illustrate angles in standard
position and coterminal angles; and
Determine the length of an arc and
area of a sector.
 Arc length is the
distance between
two points along a
section of a curve.
The length of an arc
on a circle depends
on both the angle
rotation and the
radius length of the
circle.
𝑟 𝒓𝒂𝒅𝒊𝒖𝒔
 The area of a sector is the region enclosed by
the two radii of a circle and the arc. In simple
words, the area of a sector is a fraction of the area of
the circle.
WHAT IS THE ANGLE IN STANDARD
POSITION?
 An angle is in standard
𝜃
position if the rotation
starts from the positive xaxis.
 The ray on the x – axis is
called the initial side of
the angle.
 The ray that rotates about
the center is called
terminal side.
𝛼
WHICH OF THE FOLLOWING IS AN ANGLE
IN STANDARD POSITION?
𝐹𝑖𝑔𝑢𝑟𝑒 1
𝐹𝑖𝑔𝑢𝑟𝑒 2
𝐹𝑖𝑔𝑢𝑟𝑒 3
NOTE: The location of the terminal side of the
angle determines the quadrant of the angle.
COTERMINAL ANGLES
𝛽
𝜃
𝛼
𝐹𝑖𝑔𝑢𝑟𝑒 2
𝐹𝑖𝑔𝑢𝑟𝑒 1
 Two angles in standard position that have
common terminal side are called coterminal
angles.
 Determine the
coterminal angle (one
positive and one
negative) for 210°
 Positive coterminal of 210°
1 ∙ 360°+210 ° = 570°
 Negative coterminal of 210°
−1 ∙ 360°+210 °
−360°+210 °=-150°
-150°
 Determine the
coterminal angle (two
positive and two
negative) for 120°
 Positive coterminal of 120°
1 ∙ 360°+120 ° = 480°
2 ∙ 360°+120 ° = 840°
 Negative coterminal of 120°
120°
−1 ∙ 360°+120 °
−360°+120 °=-240°
−2 ∙ 360°+120 °
−720°+120 °=-600°
15 POINTS
 Determine the
coterminal angle (two
positive and two
negative) for 70°
 Positive coterminal of 70°
1 ∙ 360°+70 ° = 430°
2 ∙ 360°+70 ° = 790°
 Negative coterminal of 70°
70°
−1 ∙ 360°+70 °
−360°+70 °=-290°
−2 ∙ 360°+70 °
−720°+70 °=-650°
 Positive coterminal
 Find the
coterminal angles
(one positive and
one negative) for
𝜋
3
 Negative coterminal
𝜃 + 2𝜋
𝜋
3
𝜋
6𝜋
= +
3
3
7𝜋
=
3
𝜃 + 2𝜋 = + 2 𝜋
𝜃 − 2𝜋
𝜋
3
𝜋
=
3
𝜃 + 2𝜋 = - 2 𝜋
-
6𝜋
3
=
−5𝜋
3
 Positive coterminal
 Find the
𝜃 + 2𝜋
coterminal angles
2𝜋
𝜃 + 2𝜋 = + 2 𝜋
(one positive and
3
2𝜋
6𝜋
one negative) for
= +
3
3
2𝜋
8𝜋
=

Negative
coterminal
3
3
𝜃 − 2𝜋
𝜃+
2𝜋
2𝜋 = - 2 𝜋
3
2𝜋 6𝜋
−4𝜋
= - =
3
3
3
15 POINTS
 Positive coterminal
 Find the
𝜃 + 2𝜋
coterminal angles
3𝜋
𝜃 + 2𝜋 = + 2 𝜋
(one positive and
2
3𝜋
4𝜋
one negative) for
= +
2
2
3𝜋
7𝜋
=

Negative
coterminal
2
2
𝜃 − 2𝜋
𝜃+
3𝜋
2𝜋 = - 2 𝜋
2
3𝜋 4𝜋
−𝜋
= - =
2
2
2
 Find the coterminal angles (one
positive and one negative) for
𝜃 + 2𝜋
 30°
 75°
 180°
2𝜋

3
𝜋

2
𝜃 − 2𝜋
 Find the coterminal angles (one
positive and one negative) for
 30° = 390°,-330
 75° = 435 °, -285
 180° = 540 °, −180
2𝜋 8𝜋 −4𝜋
 = ,
3
3
3
𝜋 5𝜋 −3𝜋
 = ,
2
2
2