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

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SUMMARY

The equation tan 2θ = -1 has solutions within the range of -180° to 180°. The primary solution identified is θ = -22.5°, derived from the fact that tan(-45°) = -1, leading to the equation 2θ = -45°. Additionally, it is important to note that the tangent function has infinitely many solutions, but the focus here is on the specified interval. Thus, the only relevant solution for θ in the given range is -22.5°.

PREREQUISITES
  • Understanding of trigonometric functions, specifically the tangent function.
  • Knowledge of angle measurement in degrees.
  • Familiarity with solving equations involving trigonometric identities.
  • Basic understanding of the periodic nature of trigonometric functions.
NEXT STEPS
  • Study the periodic properties of the tangent function to identify multiple solutions.
  • Learn how to convert between degrees and radians for broader applications.
  • Explore the unit circle to visualize trigonometric functions and their values.
  • Practice solving more complex trigonometric equations involving multiple angles.
USEFUL FOR

Students learning trigonometry, educators teaching angle measures, and anyone interested in solving trigonometric equations within specified intervals.

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 \tan(x)=-1 ?
 
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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