Question

The value of sine and cos never exceed 1,where as the value of sec and cosec are always greater than or equal to 1 .Give reasons

Answer 1

Sine and cosine always have the denominator greater than the numerator so that it never exceeds 1 , but in the case of cosecant and secant the situation is opposite,numerator is greater than denominator

Answer 2

The values of sin and cos becomes less than 1 because When we divide the leg and hypotenuse we get smaller value than 1

The value of cosec and sec becomes greater than 1 because cosecant function always produces values bigger than 1. Its value always greater than 1

Step-by-step explanation:

• Given that the values of sin and cos never exceed one
• Because the sine and cosine ratios involve dividing a leg (shortest of one side) by the hypotenuse(longest side),therefore the values will never be more than 1, when we divide the leg and hypotenuse we get smaller value than 1

• But when we compare to cosec and sec we have opposite ratios
• The hypotenuse of a right triangle larger than the leg side. And therefore, their ratio is more than 1 . Hence cosecant function always produces values bigger than 1. Its value always greater than 1