Question

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

f (x) = sin x

f (x) = cos x

f (x) = cot x

f (x) = sec x

Answer 1

We will evaluate each function separately in the given interval:
0 <x <π
f (x) = sin x
f (0) = sin 0 = 0
f (π) = sin π = 0

f (x) = cos x
f (0) = cos 0 = 1
f (π) = cos π = -1

f (x) = cot x
f (0) = cot 0 = Cos0 / sin0 = 1/0 = inf
f (π) = cot π = Cosπ / sinπ = -1 / 0 = -inf
We can observe that the function f (x) = cot x tends to infinity when it approaches zero.

f (x) = sec x
f (π / 2) = sec π / 2 = 1 / cos π / 2 = 1/0 = inf
We can observe that this function has values that tend towards infinity when it approaches π / 2

answer:
this function has values greater than 1 in 0 <x <π
f (x) = sec x