MATH SOLVE

6 months ago

Q:
# 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?

Accepted Solution

A:

Answer:c Kayla is answerStep-by-step explanation:Since sine lies between-1 and +1 we have cosecant, reciprocal of sin lying always outside -1 and 1.i.e. |cosec x|>1For acute angle sine, cos , tan are positiveSo cosec x >1 and similarly since cos x <1, sec x >1 alwaysBut tanx varies between 0 and infinity for acute anglesHence cot can take values from 0 to infinityHence the correct answer is that of 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.