What Is Secant Equal To

Secant Formula

When talking nearly whatever right-angled triangle, there are 3 sides that are, hypotenuse, perpendicular, and superlative. The side which is the largest one and is on the side which is on the opposite to the right bending is the hypotenuse. When the length of the hypotenuse is divided by the length of the next side, it gives the secant of the bending, of the right-angled triangle. Secant is denoted as 'sec'. Secant formula is derived out from the inverse cosine (cos) ratio. The secant function is the reciprocal of the cosine function, thus, the secant function goes to infinity whenever the cosine function is equal to zilch (0). The secant formula along with solved examples is explained below.

What is Secant Formula?

In the right-angled triangle, at that place are three sides i.east. Hypotenuse, the Perpendicular side (reverse), and the Next side which is the height. The largest side in the triangle is the hypotenuse, the side opposite to the bending is the perpendicular side, and the side where both hypotenuse and opposite rests is the adjacent side.

The secant function of a right triangle is its hypotenuse divided past its base. Thus, the secant formula of a given triangle can be expressed as,

sec ⁡θ = H/B

Where,

B = Base
H = hypotenuse

Also, secant is reciprocal of cos,i.e.,

sec θ = (one/cosθ)

For the secant of an angle, there is a formula related to the Pythagoras theorem, i.e.

Sec² ⁡θ = 1 + tan² ⁡θ

Notation: This equation is very useful. It is like to the squared relationship between sin ⁡θ and cos ⁡θ. (i.e. Sec² ⁡θ - tan² ⁡θ = 1)

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Examples Using Secant Formula

Instance 1: Find the side of a correct-angled triangle whose hypotenuse is fourteen units and base angle with the side is threescore degrees.

Solution:

Given,

θ = 60 caste
H = 14 units

Using the secant formula,

sec⁡θ = H/B

sec⁡60 =xiv/B

2 = 14/B

B = 14/two

B = vii

Therefore, the base side of a correct-angle triangle is 7 Units.

Case 2: Observe sec θ using the secant formula if hypotenuse = 4.9 units, the base of the triangle = four units, and perpendicular = 2.8 units.

Solution:

Given: P = two.viii, B = 4, and H = 4.9

Using the secant formula,

sec⁡θ = H/B

sec⁡θ = 4.nine/4

sec⁡θ = i.225

Therefore,sec θ is 1.225

Example iii: Find Secθ if Cosθ is given as 4/8 using a secant formula.

Solution:

Given, Cos θ = 4/8 = 1/2

Using the reciprocal secant formula,

sec θ = (i/cosθ)

secθ = 1/½

secθ = two

Therefore, secθ is 2.

FAQs on Secant Formula

What is Meant by Secant Formula?

Out of six trigonometry ratios, three ratios are basic and three are derived. Secant is one of the ratios that is derived from the cosine ratio. The secant formula helps in finding out the hypotenuse, the length, and the adjacent side of a correct-angled triangle. The formula is sec ⁡θ = H/B

What is the Formula to Find the Secant of a Right-Angled Triangle?

The secant function of a correct angle triangle is its hypotenuse divided past its base. Thus, the secant formula of a given triangle can exist expressed as,

sec ⁡θ = H/B

Where,