Final answer:
The three trigonometric reciprocals of sine, cosine, and tangent are cosecant (csc), secant (sec), and cotangent (cot).
Option a) "Cosecant, Secant, Cotangent" is the correct answer as these reciprocals are defined as 1/sin, 1/cos, and 1/tan respectively in the context of a right triangle.
Step-by-step explanation:
The three trigonometric reciprocals of sine, cosine, and tangent are cosecant, secant, and cotangent respectively. In trigonometry, these functions are defined for a right triangle as follows:
- The cosecant (csc) is the reciprocal of the sine function: csc A = 1/sin A.
- The secant (sec) is the reciprocal of the cosine function: sec A = 1/cos A.
- The cotangent (cot) is the reciprocal of the tangent function: cot A = 1/tan A.
To understand these relationships further, we recall that the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, the cosine is the ratio of the length of the adjacent side to the hypotenuse, and the tangent is the ratio of the length of the opposite side to the adjacent side in a right triangle.
Therefore, the correct answer to the question about the three trigonometric reciprocals of sine, cosine, and tangent is option a) "Cosecant, Secant, Cotangent".