Finding the range of values for tan theta > 1

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SUMMARY

The discussion focuses on determining the range of values for theta where tan(theta) > 1. The solution identifies that one interval is π/4 < theta < π/2, corresponding to 45° < theta < 90°. The periodic nature of the tangent function, with a period of π, implies that additional intervals can be derived by adding integer multiples of π to the initial range. Thus, the complete solution includes all intervals of the form (π/4 + nπ, π/2 + nπ) for any integer n.

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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?
 
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needingtoknow said:

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°.
 

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