Introduction To Terminal And Coterminal Angles
The angles that can offer same values for a trigonometry ratio are called co terminal angles for a given terminal angle
. If is the given terminal angle, then the corresponding co terminal angles of are - 3600 and 3600 + . Let, we discuss about the detailed description of the terminal and coterminal angles and its example problems. This article is very much helpful to you to know more about the terminal and coterminal angles.
Graphs of Terminal and Coterminal Angles
Let us see how we can solve a terminal and coterminal angles.
Let be 300. Then the co terminal angles are 3600 + and - 3600.
That is, 3600 + 300 = 3900 and - 3600 + 300 = -3300. Therefore, for the terminal angle 300, the co-terminal angles are 3900 and 3300. Now on looking at all the three graphs, it is clear that all the three angles -3300, 300 and 3900 represents the same angle.
terminal and coterminal angles
terminal and coterminal
terminal and coterminal angles
300
Figure (i)
Problems on Terminal and Coterminal Angles:
Let us check a trigonometry ratio for all these three angles -3300, 300 and 3900 to see that whether they give the same values.
Sin (-3300) = '1/2' ; Sin (300) = '1/2'; Sin (3900) = '1/2'.
So, as per the definition, the terminal and coterminal angles will give the same value for any trigonometrical ratios.
Infinity Number of Terminal and Coterminal Angles:
One interesting thing about the relationship among the terminal angle and its corresponding co-terminal angles is, we can find infinity number of co-terminal angles. This can be done as follows:
We know that 3600 = 2. Therefore the infinity number of co-terminal angles can be derived from (2n + ), where is the given terminal angle. Here n is an integer; It can be positive as well as negative.
Examples on Terminal and Coterminal Angles
Example 1: Find the coterminal angles of 600.
Solution:
The coterminal angles of 600 are:
(i) 360 + 60 = 4200.
(ii) 60 360 = - 3000
Answer: - 3000, 4200.
Example 2: Find the coterminal angles of -600.
Solution:
The coterminal angles of -600 are:
(i) 360 + (-60) = 3000.
(ii) - 60 360 = - 4200
Answer: - 3000, - 4200.
Practice Problems on Terminal and Coterminal Angles:
To confirm your better understanding about the terminal and coterminal angles that you have learnt just now, try the following problems:
Problem 1:
Find the coterminal angles of 450.
Answer: - 3150, 4050.
Problem 2:
Find the coterminal angles of - 450.
Answer: 3150, - 4050.
by: johnharmer
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