The exact value of the cos (17π / 12) is determined as (√2 - √6)/4
How to calculate the exact value of cos function?
The exact value of the cosine function is calculated by applying the following as shown below.
The given cosine function is
cos (17π / 12)
The function is simplified as follows;
π = 180⁰
17 π / 12 = (17 x 180⁰ ) / 12
17 π / 12 = 255⁰
Cos (255) = cos( 180 - 255)
= - cos(75)
Using trigonometry identity of cos (a + b)
cos (a + b) = cos (a) cos(b) - sin (a) sin(b)
- cos (75) = - [ cos(30 + 45)]
- [ cos(30 + 45)] = - [ cos (30) cos(45) - sin (30) sin(45) ]
- [ cos (30) cos(45) - sin (30) sin(45) ] = - [ √3/2 × √2/2 - ¹/₂ × √2/2]
The expression is simplified further as;
= - [ √3/2 × √2/2 - ¹/₂ × √2/2]
= - [√6/4 - √2/4]
= - √6/4 + √2/4
= (√2 - √6)/4