The value of
(secpi/7)+(sec3pi/7)+(sec5pi/7) is
To find the value of (sec(pi/7) + sec(3pi/7) + sec(5pi/7)), we'll start by understanding what the secant function represents.
The secant function (sec(x)) is the reciprocal of the cosine function (cos(x)). Mathematically, sec(x) can be defined as:
sec(x) = 1 / cos(x)
Now, let's determine the values of sec(pi/7), sec(3pi/7), and sec(5pi/7) individually.
1. sec(pi/7):
To find sec(pi/7), we need to calculate cos(pi/7) and then take its reciprocal.
cos(pi/7) is a trigonometric value that might not have a simple numerical expression. Instead, we can calculate its decimal approximation as follows:
cos(pi/7) ≈ 0.62349
Therefore, sec(pi/7) = 1 / cos(pi/7) ≈ 1.60186
2. sec(3pi/7):
Similarly, we need to calculate cos(3pi/7) and take its reciprocal.
cos(3pi/7) is another trigonometric value that might not have a simple numerical expression. We can calculate its decimal approximation as follows:
cos(3pi/7) ≈ -0.22252
Therefore, sec(3pi/7) = 1 / cos(3pi/7) ≈ -4.48467
3. sec(5pi/7):
Again, we need to calculate cos(5pi/7) and take its reciprocal.
cos(5pi/7) is also a trigonometric value that might not have a simple numerical expression. We can calculate its decimal approximation as follows:
cos(5pi/7) ≈ -0.94154
Therefore, sec(5pi/7) = 1 / cos(5pi/7) ≈ -1.06225
Now that we have the values of sec(pi/7), sec(3pi/7), and sec(5pi/7) approximated, we can sum them up:
(sec(pi/7) + sec(3pi/7) + sec(5pi/7)) ≈ (1.60186 + (-4.48467) + (-1.06225)) ≈ -3.94506
Hence, the value of (sec(pi/7) + sec(3pi/7) + sec(5pi/7)) is approximately -3.94506.
I saw this before,
I know the answer is exactly 4 , but at the moment I cannot see how to show that.
Been messing around with it for a while,