# Coterminal Angles: Examples

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Videos, worksheets, solutions, and activities to help Algebra 2 students learn about coterminal angles.

How to determine if Two Angles Are Coterminal?
How to find angles that are coterminal to a given angle?

How to plot angles in standard position and coterminal angles?
An angle is in standard position if its vertex is at the origin and the initial side is on the positive x-axis.
An angle in standard position is said to lie in the quadrant in which its terminal side lies.
Angles in standard position having their terminal sides along the x-axis or y-axis, such as angles with measures 90°, 180°, 270°, and so on, are called quadrantal angles.
Coterminal angles are angles in standard position that have a common terminal side. For example 30°, 390° and -330° are all coterminal.

Example:

1. Find 2 angles that are coterminal with 135°.
2. Find the angles of least positive measure coterminal to each angle.
a) 1070°
b) -65°
3. What would be an expression you could use to express all angles coterminal to 90°?

How to find Coterminal Angles?
What it means for two angles to be coterminal, and discuss a quick method on how to decide if two angles are in fact coterminal. Examples of finding angles that are coterminal to each other.
Example:
a) Which of the following angles is coterminal with an angle of 136°?
b) Which of the following angles is coterminal with an angle of -255°?

How to decide if angles are coterminal or not?
Example:
a) Which of these is not a pair of coterminal angles?
(i) -400°, -40°
(ii) 340°, -50°

b) Which of these is not a pair of coterminal angles?
(i) 4°, 724°
(ii) -15°, -385°

How to find angles that are coterminal to a given angle that also satisfy other conditions?
(finding the smallest positive coterminal angle and finding the negative angle closest to zero that is coterminal with a given angle).
a) What is the smallest positive angle that can be coterminal with 575°
b) Find the negative angle closest to zero and coterminal with θ = 635°

Example:
Determine if Two Angles Are Coterminal
Are 132° and -588° coterminal?

How to determine Coterminal Angles in Radian Measure?
Example:
Determine a positive an negative angle that is coterminal to the given angle
a) π/3
b) -4π/5

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