Final answer:
The right-angled triangle with side lengths 1, 1, and √2 best illustrates the concepts of cosecant, secant, and cotangent, as it simplifies the computation of these reciprocal trigonometric functions.
Step-by-step explanation:
When discussing the concepts of cosecant, secant, and cotangent, which are the reciprocal trigonometric functions of sine, cosine, and tangent respectively, it is ideal to illustrate these concepts using a right-angled triangle where all sides and angles are known or easily calculated. The triangle that best illustrates these concepts is:
- b) A right-angled triangle with side lengths 1, 1, and √2
This is because the sides of this triangle allow for the easiest computation of trigonometric functions. For instance, in a right-angled triangle where the sides are 1, 1, and √2:
- The sine of an angle would be 1/√2, and thus the cosecant (reciprocal of sine) would be √2.
- The cosine of an angle would also be 1/√2, making the secant (reciprocal of cosine) also √2.
- The tangent of an angle would be 1/1, so the cotangent (reciprocal of tangent) would also be 1.
This triangle simplifies the calculation and understanding of these trigonometric ratios due to its special 45°-45°-90° angles, where the ratios of the sides remain consistent.