The secant (sec) formula in trigonometry is sec(θ) = hypotenuse / adjacent, where θ is an angle in a right-angled triangle.
Here's a breakdown:
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Secant (sec θ): A trigonometric function that is the reciprocal of the cosine function.
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Right-Angled Triangle: A triangle containing one angle of 90 degrees.
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Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
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Adjacent: The side of the right-angled triangle that is next to the angle θ (and is not the hypotenuse).
Relationship to Cosine:
Since secant is the reciprocal of cosine, we can write:
sec(θ) = 1 / cos(θ)
And because cos(θ) = adjacent / hypotenuse, this confirms:
sec(θ) = hypotenuse / adjacent
Example:
Imagine a right-angled triangle where the angle θ is formed by the adjacent side, which measures 4 units, and the hypotenuse, which measures 5 units. To find sec(θ):
sec(θ) = 5 / 4 = 1.25
Mnemonic:
A common mnemonic device to remember trigonometric ratios is SOH CAH TOA:
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
From CAH, and knowing that secant is the reciprocal of cosine, we can easily derive that secant is Hypotenuse / Adjacent.
