Cosine: Value
How to find the value of cosine (trigonometry): 1 example and its solution. + Cosine values of commonly used angles.
Example
Example
Solution
First, find the reference angle of 4π/3.
4π/3 is between π and 3π/2.
So draw the terminal side on quadrant III.
Then the reference angle is
4π/3 - π.
-π = -3π/3
4π/3 - 3π/3 = π/3
So the reference angle is π/3.
Draw a right triangle like this.
The central angle is π/3: 60º.
So this is a 30-60-90 triangle.
So the base is -1.
The height is -√3.
And the hypotenuse is 2.
cos 4π/3 is the cosine of the right triangle.
Cosine is CAH:
Cosine,
Adjacent side (-1),
Hypotenuse (2).
So cos 4π/3 = -1/2.
Write the minus sign
in front of the fraction.
So cos 4π/3 = -1/2.
Cosine Values of Commonly Used Angles
Table
These are the cosine values
of commonly used angles.
Detail
θ = 0
The adjacent side (base) is 1.
The opposite side (height) is 0.
The hypotenuse is 1.
CAH:
Cosine,
Adjacent side (1),
Hypotenuse (1).
So cos 0 = 1/1 = 1.
θ = π/6
This is a 30-60-90 triangle.
The adjacent side (base) is √3.
The opposite side (height) is 1.
The hypotenuse is 2.
CAH:
Cosine,
Adjacent side (√3),
Hypotenuse (2).
So cos π/6 = √3/2.
θ = π/4
This is a 45-45-90 triangle.
The adjacent side (base) is 1.
The opposite side (height) is 1.
The hypotenuse is √2.
CAH:
Cosine,
Adjacent side (1),
Hypotenuse (√2).
So cos π/4 = 1/√2 (= √2/2).
θ = π/3
This is a 30-60-90 triangle.
The adjacent side (base) is 1.
The opposite side (height) is √3.
The hypotenuse is 2.
CAH:
Cosine,
Adjacent side (1),
Hypotenuse (2).
So cos π/3 = 1/2.
θ = π/2
The adjacent side (base) is 0.
The opposite side (height) is 1.
The hypotenuse is 1.
CAH:
Cosine,
Adjacent side (0),
Hypotenuse (1).
So cos π/2 = 0/1 = 0.