Four students wrote statements about cosecant, secant, and cotangent values as shown below.AnikThe cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.IsabellaThe cosecant, secant, and cotangent of an acute angle are always greater than 1.KaylaThe cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.MorrisThe cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.Which student is correct?
For an acute angle, both sine and cosine are between 0 and 1, so their reciprocals, cosecant and secant, are always greater than 1. Cotangent is cosine divided by sine: it is greater than 1 for angles below 45°, equal to 1 at 45°, and less than 1 for angles above 45°. Therefore, Kayla is correct.
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