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

  • Thread starter lionely
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In summary, the conversation involves finding the value of theta for which tan(theta)=-1, with a range specified between -180 and 180 degrees. The conversation also touches on the concept of working in radians and the fact that there are infinitely many solutions to the equation. Finally, the conversation concludes with the realization that theta would be -22.5 degrees within the specified range.
  • #1
lionely
576
2
tan 2θ= -1

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

ranging between -180 and 180
 
Last edited:
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  • #2
For what value of x does [itex]\tan(x)=-1[/itex] ?
 
  • #3
I believe -45
 
  • #4
deleted
 
Last edited:
  • #5
lionely said:
I believe -45

Is that the only value??
 
  • #6
Yes what are the possible values of theta and I'm sure, I haven't started working in radians at school as yet... =/
 
  • #7
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?
 
  • #8
Theta would be -22.5 oh and I forgot to mention the question asked between -180 and 180 sorry.
 

1. What is the meaning of "Tan 2θ"?

"Tan 2θ" refers to the tangent of an angle, where θ represents the measure of the angle. In this case, the angle is multiplied by 2 and the tangent is taken, resulting in a numerical value.

2. What is the range of solutions for "Tan 2θ"?

The range of solutions for "Tan 2θ" is between -180 and 180. This represents all possible angles, both positive and negative, in degrees.

3. How do you find solutions for "Tan 2θ" within the given range?

To find solutions for "Tan 2θ" within the range of -180 and 180, you can use a scientific calculator or a trigonometric table. Simply input the desired angle in degrees and take the tangent to find the solution.

4. Can "Tan 2θ" have multiple solutions within the given range?

Yes, "Tan 2θ" can have multiple solutions within the range of -180 and 180. This is because the tangent function is periodic, meaning it repeats itself infinitely. So, there can be multiple angles that result in the same tangent value.

5. Is it possible for "Tan 2θ" to have no solutions within the given range?

Yes, it is possible for "Tan 2θ" to have no solutions within the range of -180 and 180. This can happen when the tangent value is undefined or when there is no angle that results in the given tangent value.

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