What is the exact value of the cos of 23pi/12?
(Twenty-three pi over 12, which is = to 345 degrees.)
Thank you,
Roger
cos 23π/12 = cos 345°
= cos 15° ( we are 15° from the x-axis in quadrant IV, and the cosine in IV is positive)
I know cos 2A = 2cos^2 A - 1
or
cos 30° = 2cos^2 15 - 1
√3/2 + 1 = 2cos^2 15
(√3 + 2)4 = cos^2 15
cos 15 = [√(√3+2)]/2
To find the exact value of cos(23π/12), we can start by converting 23π/12 to degrees.
We know that π radians is equivalent to 180 degrees. So to convert radians to degrees, we can use the following conversion factor:
1 radian = 180 degrees / π
Now, let's convert 23π/12 to degrees:
23π/12 * (180 degrees / π) = (23 * 180) / 12 = 390 degrees
So, cos(23π/12) is equivalent to cos(390 degrees).
To find the exact value of cos(390 degrees), we can use the unit circle. Since the cosine function gives the x-coordinate of a point on the unit circle, we need to look for the x-coordinate of the angle 390 degrees.
Looking at the unit circle, we can see that the angle 390 degrees is in the fourth quadrant, where cosine is positive.
Knowing that cos(0 degrees) = 1, we can see that cos(360 degrees) = 1 as well. This means that cos(390 degrees) is equivalent to cos(390 degrees - 360 degrees) = cos(30 degrees).
Now, we know that cos(30 degrees) = √3/2.
Therefore, the exact value of cos(23π/12) is √3/2.
Let me know if you need help with anything else!