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What Does Cosecant Mean in Algebra 2?

What Does Cosecant Mean in Algebra 2? thumbnail
The sun's angular position is calculated using trigonometry and the shadow's length.

Trigonometry is the study of the mathematical relations among the sides and angles of triangles. The cosecant is one of six trigonometric ratios defined for the lengths of the sides of a right triangle.

  1. Right Triangles

    • A right triangle has one right angle (90-degree angle) and two acute (less than 90 degrees) angles. The longest side of a right triangle is the hypotenuse, which lies across from (opposite to) the 90-degree angle. The trigonometric ratios are defined for the two acute angles.

    Notation

    • For each acute angle, the hypotenuse (notated as hyp in equations) forms one side of the angle; the other side of the angle is called the adjacent (adj) side. The third side of the triangle is designated as the side opposite (opp) the angle.

    Trigonometric Ratios

    • The cosecant of angle A is the ratio of the length of the hypotenuse to the length of the side opposite angle A (cosecant A = hyp/opp). This is the inverse of sine A = opp/hyp. The other trigonometric ratios are cosine A = adj/hyp, tangent A = opp/adj and their respective inverses, secant A = hyp/adj and cotangent A = adj/opp.

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