Please help, I know cos 72 degrees = (sqrt 5 - 1)/4.
I need to know what cos 36 degrees is. How to do so?
since cos2x = 2cos^2 x - 1,
cos 36 = sqrt((1+cos 72)/2)
thx
To find the value of cos 36 degrees, you can make use of the formula for the double-angle identity of the cosine function.
The formula states that cos(2x) = 2cos^2(x) - 1.
To utilize this formula, we need to express 36 degrees in terms of its double angle, which is 2 times some angle. In this case, we can express 36 degrees as 2 times 18 degrees.
Now, let's denote x as 18 degrees. Plugging this into the double-angle identity formula, we can find the value of cos 36 degrees.
cos(36 degrees) = cos(2x) = 2cos^2(x) - 1
cos(36 degrees) = 2*cos^2(18 degrees) - 1
However, to find the exact value of cos(18 degrees), we can make use of a trigonometric identity called the golden ratio identity, also known as the pentagon identity. This identity states that cos(36 degrees) = (sqrt(5) + 1) / 4.
By substituting this value into the equation we derived earlier, we get:
cos(36 degrees) = 2*(sqrt(5) + 1)/4 - 1
Simplifying this expression, we get:
cos(36 degrees) = (sqrt(5) + 1)/2 - 1/2
cos(36 degrees) = (sqrt(5) + 1 - 1) / 2
cos(36 degrees) = sqrt(5) / 2
So, cos(36 degrees) = sqrt(5) / 2.
Therefore, the value of cos 36 degrees is sqrt(5) / 2.