Finding the range of values for tan theta > 1

[needingtoknow]

Homework Statement

How to find the values of theta that make tan theta > 1 true?

The Attempt at a Solution

From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to special triangles that tan45 = 1 but I don't know how that tells me the range, all that tells me is that tan theta ≠ 45. Is there a systematic process of finding the range of values?

 

[Mark44]

Homework Statement

How to find the values of theta that make tan theta > 1 true?

The Attempt at a Solution

From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to special triangles that tan45 = 1 but I don't know how that tells me the range, all that tells me is that tan theta ≠ 45. Is there a systematic process of finding the range of values?

The tangent function is periodic with period $\pi$. One interval for which tan(θ) > 1 is $\pi/4 < \theta < \pi/2$. Can you figure out what all such intervals would be, given that the period is $\pi$.

Note that radian measure is used more often in mathematics than degree measure. $\pi/4$ = 45°.