Focused Calculator
Secant Ratio Calculator
Find sec(A) by comparing hypotenuse c with adjacent side b, the reciprocal of cosine.
Calculate Secant Ratio
이 계산기는 공식을 사용하며 sec(A) 값을 구합니다.
sec(A) 값을 구하려면 값을 입력하세요.
sec(A)
결과-
풀이 과정
공식:
How This Secant Ratio Calculator Works
Secant is the reciprocal of cosine. Where cosine divides the adjacent side by the hypotenuse, secant flips that — it divides the hypotenuse by the adjacent side. The result is always greater than or equal to 1 because the hypotenuse is always the longest side in a right triangle.
This calculator takes two inputs — hypotenuse c and adjacent side b — and returns sec(A). It is a quick way to get this reciprocal ratio without doing the division by hand or computing cosine first.
Enter the hypotenuse c and adjacent side b in the fields above. The calculator computes sec(A) = c / b. Both values must be positive, and c must be greater than b.
Formula
Secant of angle A equals the hypotenuse divided by the adjacent side. This is the reciprocal of cosine: sec(A) = 1 / cos(A).
Because the hypotenuse is always longer than the adjacent side in a right triangle, sec(A) is always greater than 1. As angle A gets larger, the adjacent side shrinks relative to the hypotenuse, so secant increases.
Triangle Diagram
For angle A, side a is opposite, side b is adjacent, and side c is the hypotenuse.
Secant uses the hypotenuse c as the numerator and the adjacent side b as the denominator. The opposite side a is not part of the secant calculation.
Ratio Highlight
Secant uses the hypotenuse c as the numerator and the adjacent side b as the denominator. The opposite side a is not part of the secant calculation.
Side Key
- a = Opposite (height across from angle A) Not used in sec(A)
- b = Adjacent (base next to angle A) Used in sec(A)
- c = Hypotenuse (slanted side) Used in sec(A)
The minimum value of secant in a right triangle is slightly above 1, which occurs when angle A is very small and the adjacent side is nearly as long as the hypotenuse. As angle A increases, the adjacent side shortens relative to the hypotenuse, and secant grows larger.
How to Use
- Identify angle A in your right triangle.
- Find side c, the hypotenuse: the longest side, across from the right angle.
- Find side b, the adjacent leg: the side that touches both angle A and the right angle.
- Enter c in the first input field.
- Enter b in the second input field.
- Click Calculate.
- The result is sec(A), which is always greater than or equal to 1.
Step-by-Step Example
A right triangle has hypotenuse c = 5 and adjacent side b = 4.
The secant of angle A is 1.25. To verify: cos(A) = 4 / 5 = 0.8, and 1 / 0.8 = 1.25.
What the Result Means
Secant tells you how many times longer the hypotenuse is compared to the adjacent side. A secant of 1.25 means the hypotenuse is 25% longer than the adjacent side.
The minimum value of secant in a right triangle is slightly above 1, which occurs when angle A is very small and the adjacent side is nearly as long as the hypotenuse. As angle A increases, the adjacent side shortens relative to the hypotenuse, and secant grows larger.
Secant is useful whenever you need to scale from the adjacent side to the hypotenuse, or when a formula calls for 1 / cos(A).
When to Use This Ratio
This secant ratio calculator is the right choice when:
- A formula requires secant or 1 / cos(A) and you want the value directly.
- You need to find how much longer the hypotenuse is compared to the adjacent side.
- You are working with calculus problems that involve secant in derivatives or integrals.
- You are checking structural calculations where the hypotenuse represents the actual length and the adjacent side represents the horizontal projection.
Common Mistakes
These secant errors trip up students most often:
- Confusing secant with cosine. Cosine is b / c (adjacent over hypotenuse). Secant is the reciprocal: c / b (hypotenuse over adjacent).
- Getting a result less than 1. If your answer is below 1, you likely reversed the fraction. In a valid right triangle, sec(A) is always greater than or equal to 1.
- Using the opposite side instead of the adjacent side. Secant pairs the hypotenuse with the adjacent side, not the opposite side.
- Mixing up secant and cosecant. Secant is the reciprocal of cosine. Cosecant is the reciprocal of sine. They use different sides.
- Entering b larger than c. The hypotenuse must always be longer than the adjacent side.
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What is the secant ratio in a right triangle? expand_more
Secant is defined as sec(A) = c / b, where c is the hypotenuse and b is the adjacent side. It is the reciprocal of cosine.
02 시컨트가 항상 1보다 큰 이유는 무엇입니까? expand_more
직각삼각형에서 빗변 c는 항상 변 중 가장 길기 때문입니다. 더 큰 숫자(c)를 더 작은 숫자(b)로 나누면 항상 1보다 큰 결과가 나옵니다.
03 시컨트와 코사인을 어떻게 변환합니까? expand_more
sec(A) = 1 / cos(A)이고, cos(A) = 1 / sec(A)입니다. 하나를 알고 있으면 역수를 취하여 다른 하나를 찾을 수 있습니다.
04 초(45°)란 무엇입니까? expand_more
45-45-90 삼각형에서 빗변은 다리의 √2배입니다. 따라서 sec(45°) = √2 ≒ 1.4142입니다.
05 실제 응용 프로그램에서 시컨트가 사용됩니까? expand_more
예. 시컨트는 물리학 공식, 공학 계산 및 미적분학에 나타납니다. 경사를 따라 수평 거리를 실제 경로 길이로 조정해야 할 때 사용됩니다.