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Which of the following trigonometric functions, restricted to 0 < x < π, have values greater than 1?

a.) f(x) = sin x

b.) f(x) = cos x

c.) f(x) = cot x

d.) f(x) = sec x

Verified Answer :

Answer:  The answer is (c) f(x) = cos x and f(x) = sec x.

Step-by-step explanation: We are given four trigonometric functions out of we are to select those which have values greater than for 0 < x < π.

Since the values of sine and cosine functions lies between -1 and 1. So, they cannot go beyond 1 and hence option (a) and (b) are incorrect.

Since \(\tan \dfrac{\pi}{6}=\dfrac{1}{\sqrt 3},\)

so we will have

\(\cot \dfrac{\pi}{6}=\sqrt {3}>1.\)

So, option (c) is correct.

And, we know that

\(\cos \dfrac{\pi}{6}=\dfrac{\sqrt 3}{2},\)

so we will have

\(\sec \dfrac{\pi}{6}=\dfrac{2}{\sqrt {3}}>1.\)

So, this option is also correct.

Thus, (c) and (d) are the correct ones.

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