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Reciprocal Trigonometric Functions The three remaining trigonometric ratios are the reciprocals of the first three. You may think of them as the first three turned upside down, or what you must multiply the first three by in order to get a product of 1. The reciprocal of the sine is cosecant, abbreviated csc. Secant is the reciprocal of cosine and is abbreviated sec. Finally, cotangent, abbreviated cot, is the reciprocal of tangent. 30 CliffsStudySolver Trigonometry θ p a hy θ b n ote opposite side use c adjacent side (a) (b) Models for reciprocal trigonometric ratios.

That side is half the length of the hypotenuse, so the hypotenuse must be twice the length of that side, or 10 in. Finally, the side opposite the 60° angle (the other leg) is half the hypotenuse times the square root of three. 3. In triangle ABC, with right angle at B, the cosine of ∠A is 11 . What is the sine ∠C? 15 11 answer: 15 The cofunction identities tell us that in a given right triangle, the sine of one acute angle is the cosine of the other. Work Problems Use these problems to give yourself additional practice.

Answer: 3 opposite The tan ratio is adjacent . 3 3 cm is the length of the side opposite ∠β, and its 3 3 adjacent side is 3 cm. So, tan b = 3 = 3 . Reciprocal Trigonometric Functions The three remaining trigonometric ratios are the reciprocals of the first three. You may think of them as the first three turned upside down, or what you must multiply the first three by in order to get a product of 1. The reciprocal of the sine is cosecant, abbreviated csc. Secant is the reciprocal of cosine and is abbreviated sec.