sec(15[pi])/(8)
15[pi])/(8) radians = 337.5 degrees
or -22.5 degrees
15[pi])/(8
= sec 337.5 dgs
= sec (-22.5) dgs
= sec 22.5 dgs
= 1/cos 22.5 dgs
so let's find cos 22.5
cos 2A = 2cos^2 A - 1
cos 45 = 2cos^2 22.5 - 1
(√2/2 + 1)/2 = cos^2 22.5
(√2 + 2)/4 = cos^2 22.5
cos 22.5 = √(√2+2)/2
sec 22.5 = 2/√(√2+2)
sec(15[pi])/(8) = 2/√(√2+2)
To find the value of sec(15π)/8, we need to understand the properties and definition of secant function.
The secant function is the reciprocal of the cosine function. It is defined for all real numbers except where cosine is zero. The formula for secant is:
sec(x) = 1 / cos(x)
In the given expression, we have sec(15π)/8. So, first, let's find the value of cos(15π):
cos(15π) is the cosine of 15π. Recall that the cosine function has a period of 2π, which means cos(x) = cos(x + 2πn), where n is any integer.
Therefore, cos(15π) = cos(15π - 2π) = cos(13π). We can continue subtracting 2π or add 2π until we are within the range of 0 to 2π.
cos(13π) = cos(13π - 2π) = cos(11π)
cos(11π) = cos(11π - 2π) = cos(9π)
cos(9π) = cos(9π - 2π) = cos(7π)
cos(7π) = cos(7π - 2π) = cos(5π)
cos(5π) = cos(5π - 2π) = cos(3π)
cos(3π) = cos(3π - 2π) = cos(π)
Now, cos(π) = -1, so we have:
sec(15π)/8 = 1/cos(π)/8
Simplifying further:
sec(15π)/8 = 1/(-1)/8 = -1/8
Therefore, the value of sec(15π)/8 is -1/8.