Concept

Secant

θ

of a right triangle, the secant of

θ

is the ratio between the lengths of the hypotenuse and the adjacent side.

The secant of

θ

is written as

sec (θ) .

$sec (θ) = \frac{hypotenuse}{adjacent}$

This trigonometric ratio states the ratio between the hypotenuse and the adjacent side to a certain angle. It gives no indication about the lengths of the sides.

Right triangle with two vertices movable and the secant of one acute angle is computed while the measures change

When the adjacent side and hypotenuse lengths change for a given angle, if their ratio stays the same then the secant, too, would stay the same. Also note that the secant of

θ

is the reciprocal of the cosine of

θ .

⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ sec θ = \frac{hyp}{adj} \frac{∣}{∣} cos θ = \frac{adj}{hyp} \frac{\frac{∣}{∣}}{∣} \Rightarrow sec θ = \frac{1}{cos θ}

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