Question

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

Answer 1

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 (\pi)/(6)=(1)/(\sqrt 3),`

so we will have

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

So, option (c) is correct.

And, we know that

`\cos (\pi)/(6)=(\sqrt 3)/(2),`

so we will have

`\sec (\pi)/(6)=\frac{2}{\sqrt {3}}>1.`

So, this option is also correct.

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