No, secant (sec) is not the opposite of cosine (cos); it's the reciprocal of cosine.
Here's a breakdown:
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Reciprocal Relationship: The secant of an angle is defined as 1 divided by the cosine of that angle. Mathematically, sec(x) = 1/cos(x).
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Opposite vs. Reciprocal: "Opposite" implies subtraction or negation (like additive inverses). "Reciprocal" means multiplicative inverse (flipping the fraction).
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Example:
Angle (x) cos(x) sec(x) = 1/cos(x) 0° 1 1 30° √3/2 ≈ 0.866 2/√3 ≈ 1.155 45° √2/2 ≈ 0.707 2/√2 ≈ 1.414 60° 1/2 = 0.5 2 90° 0 Undefined -
In a Right Triangle (SOH CAH TOA):
- cos(x) = Adjacent / Hypotenuse
- sec(x) = Hypotenuse / Adjacent
Therefore, secant is the multiplicative inverse (reciprocal), not the additive inverse (opposite), of cosine.
