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1800-102-2727The word secant comes from the Latin word secare, meaning to cut. So secant is also referred to as the intersecting lines inside a circle. But that is another case. Here, we are referring to the secant angle in trigonometry.Secant of any angle or sec x is defined as the ratio of the length of hypotenuse to the adjacent side of the angle for which secant angle is to be found out. Secant is the inverse of cosine (generally known as cos). Secant angle is positive in the 4th quadrant. Sec 0 = 1/cos 0
Since secant is the inverse of the cosine function, therefore, it is infinity wherever the cosine function is zero.
Derivative of secant function
The derivative of a secant function is sec(x) tan (x).
According to trigonometry, the value of sec 0 is 1.
Proof –
Consider a right-angled triangle PQR with angle P as the secant angle for which we need to find sec 0.
According to the secant definition, sec of angle P = length of the hypotenuse/length of the adjacent side
= PQ/PR
Since angle P will be zero, this implies that the value of the length PQ will be equal to the length of PR.
Therefore, sec 0 = PR/PR, which gives the value of sec 0 = 1.
Hence, proved.
Also, cos 0 is 1. The inverse of cos 0 will be 1.
Sec 0 = 1/cos 0 = 1/1 = 1
The inverse of a secant function is known as the arcsec function. Whenever we see arcsec A written, we can infer the angle whose secant is A.
arcsec x = sec-1 x
sec 60 = 2.000 Means: The secant of 60 degrees is 2.000
arcsec 2.0 = 60 Means: The angle whose secant is 2.0 is 60 degrees.
sec 2 y = 1 + tan 2 y
sec(90°–x) = x
sec(2x) = x/(2–x)
Find the secant angle of W.
Solution
According to the definition, sec W = hypotenuse / base of angle W
Here, hypotenuse is WV = 37 (hypotenuse is always the opposite line of the right angle)
Base of angle W is WU = 12
Therefore, sec W = 37/12
If the value of angle W is 0, then there will be no triangle. Only the straight line WU will be present. This implies that the value of sec 0 will be 1.