Tan 2θ: Solutions between -180 and 180".

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Homework Help Overview

The discussion revolves around solving the equation tan 2θ = -1, specifically looking for solutions within the range of -180 to 180 degrees. Participants are exploring the properties of the tangent function and its periodic nature.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to identify values of θ that satisfy the equation, with some questioning whether -45 degrees is the only solution. There is discussion about the periodic nature of the tangent function and whether all solutions within the specified range are required.

Discussion Status

The conversation is ongoing, with participants sharing their thoughts on potential solutions and the implications of the periodicity of the tangent function. Some guidance has been offered regarding the relationship between 2θ and θ, but no consensus has been reached on the complete set of solutions.

Contextual Notes

There is mention of participants not having started working with radians yet, which may influence their understanding of the problem. The range of solutions is explicitly noted as being between -180 and 180 degrees.

lionely
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tan 2θ= -1

I don't understand how to work this question could someone walk me through it?

ranging between -180 and 180
 
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For what value of x does [itex]\tan(x)=-1[/itex] ?
 
I believe -45
 
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Last edited:
lionely said:
I believe -45

Is that the only value??
 
Yes what are the possible values of theta and I'm sure, I haven't started working in radians at school as yet... =/
 
lionely said:
Yes what are the possible values of theta and I'm sure, I haven't started working in radians at school as yet... =/

Ok so you know that there are infinitely many solutions to tan(x)=-1 right? Because just like how the sin and cos graphs go on forever, the tan function does as well. Anyway, are you expected to find all the solution for θ between -180o and 180o?

And another thing, if tan(-45o)=-1 and we have that 2θ=-45o then what is θ?
 
Theta would be -22.5 oh and I forgot to mention the question asked between -180 and 180 sorry.
 

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