Call Now
1800-102-2727Sine, cosine, and tangent are the three essential trigonometric functions. The other three trigonometric functions are derived from these three functions, namely secant, cosecant, and cotangent, commonly known as a sec, cosec, and cot.
Secant is also the reciprocal of the cosine function. It is the ratio of the length of the hypotenuse to the length of the adjacent side of the angle considered in a right-angled triangle.
Secant = hypotenuse / base of the angle considered
From the given diagram, we can see sec alpha = hypotenuse / base of the right-angled triangle.
This gives, sec ∠α = h/b
Also, sec ∠α = 1/cos ∠α
Therefore, sec 30 = 1/cos 30
We know the value of cos 30 = √3/2
Hence, the value of sec 30 = 2/√3
Find the value of (2 sec 30° + 2 cos 60°).
Solution
We know, sec 30° = 2/√3 and cos 60° = 1/2
Therefore, 2 sec 30° + 2 cos 60° = 2 × 2/√3 + 2 × ½
= 4/√3 + 1
2 sec 30° + 2 cos 60° = 4/√3 + 1
Find the value of Cos 30° x Sec 30° - Sec² 30°.
Solution
Cos 30° x Sec 30° - Sec² 30° = 3/√2 × 2/√3 − (3/√2)²
= 1 – ¾ = ¼
0° | 30° | 45° | 60° | 90° | |
Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
Cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
Tan | 0 | 1/√3 | 1 | √3 | ∞ |
Sec | 1 | 2/√3 | √2 | 2 | ∞ |
Cosec | ∞ | 2 | √2 | 2/√3 | 1 |
Cot | ∞ | √3 | 1 | 1/√3 | 0 |
sec 2 y = 1 + tan 2 y
sec(90°–x) = x
sec(2x) = x/(2–x)
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.