Sec 30
The value of Sec 30 degrees is equal to 2/√3. In trigonometry, you may have learned about three main primary functions, such as sine, cosine and tangent along with them the other three trigonometric functions, such as secant, cotangent and cosecant. Here, you will find the value of sec 30 degrees along with the other secant degree values.
Secant function is the transpose of the cosine function. Therefore, to find the value of sec 30, we have to find the value of cos 30. We take the reference of a right-angle triangle to get the values of trigonometric functions or ratios such as sin, cos, tan, sec, cot, csc.
value of sec 30° = 2/√3
As we know, Cosine function defines a relation between the adjacent side and the hypotenuse of a right-angled triangle with respect to the angle, formed between the adjacent side and the hypotenuse. Therefore, we can say the secant function defines a relation between the hypotenuse and adjacent side of the right-angled triangle with respect to the angle, formed between the adjacent side and the hypotenuse. Hence, the sec 30° value will be the ratio of the hypotenuse and adjacent side.
We will derive the value of sec 30 degrees with the help of cos function. Also, the values of other degrees such as 0°, 45°, 60°, 90°^{ }which are generally used in trigonometry equations.
What is Sec 30 Value?
We know that, in a right-angled triangle, the secant of ∠α is a ratio of the length of the hypotenuse and the adjacent side to the angle, where ∠α is the angle formed between the adjacent side and the hypotenuse.
secant ∠α = Hypotenuse/Adjacent Side
= Hypotenuse/Base
sec ∠α = h/b
The value of sec 30 degrees is 2√3.
The value of sec 30 in radians is π/180°.
Let us derive the value of secant 30 in the next section.
Derivation of Sec 30 Degrees
Since, we know,
sec A = 1/cos A
From the above figure, in triangle ABD,
sec 30^{0} = 1/cos 30^{0}
Since the value of cos 30^{0} = √3/2
Hence, the value of sec 30^{0} = 2/√3
In the same way, we can write the other values sec ratios, such as,
sec 0^{0} = 1/cos ^{0}= 1/1 = 1
sec 45^{0} = 1/cos 45^{0} = 1/1/√2 = √2
sec 60^{0} = 1/cos 60^{0} = 1/1/2= 2
sec 90^{0} = l/cos 90^{0} = 1/0= ∞
Given below is the trigonometry table for the trigonometric ratios covering the values of degrees 0^{0}, 30^{0}, 45^{0}, 60^{0}, 90^{0}.
0^{0} | 30^{0} | 45^{0} | 60^{0} | 90^{0} | |
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 | ∞ |
Csc | ∞ | 2 | √2 | 2/√3 | 1 |
Cot | ∞ | √3 | 1 | 1/√3 | 0 |
Sec 30 Example Problem
Example: Compute 2 sec 30^{0} + 2 cos 60^{0}.
Solution:
Given,
2 sec 30^{0} + 2 cos 60^{0}
We know, sec 30^{0} = 2/√3 and cos 60^{0} = 1/2
Therefore,
2 sec 30^{0} + 2 cos 60^{0} = 2 × 2/√3 + 2 × ½
= 4/√3 + 1
2 sec 30^{0} + 2 cos 60^{0}= 4/√3 + 1.
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Related links | |
Sin 30 degrees | Tan 30 Degrees |
Trigonometric Identities | Trigonometric Functions |
Trigonometry Formulas | Trigonometric Equations |