Inverse Trigonometric Problem Solve equation for x

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SUMMARY

The equation arctan(8x-8) = -1 can be solved by applying the tangent function to both sides, resulting in 8x - 8 = tan(-1). The correct simplification leads to x = (1/8)(tan(-1) + 8). Users must ensure their calculators are set to radians mode to avoid incorrect results. The final answer, rounded to three decimal places, is x = 0.805.

PREREQUISITES
  • Understanding of inverse trigonometric functions, specifically arctan
  • Proficiency in using the tangent function and its properties
  • Ability to manipulate algebraic equations
  • Familiarity with calculator settings, particularly radians vs degrees
NEXT STEPS
  • Learn how to convert between radians and degrees in trigonometric calculations
  • Study the properties of inverse trigonometric functions
  • Practice solving equations involving arctan and other inverse functions
  • Explore the use of graphing calculators for trigonometric equations
USEFUL FOR

Students tackling trigonometry homework, educators teaching inverse functions, and anyone needing to solve equations involving arctan.

chapsticks
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Homework Statement



arctan(8x-8)=-1

Homework Equations



I'm sure what this part wants.

The Attempt at a Solution



tan[arctan(8x-8)]=tan(-1)
8x-8=tan(-1)
x=(1/8)(tan(-1)+8)
x=(1/8)(-(tan(1)+8)
x=

I am stuck on the last part since the homework says Simplify the above equation. (Round your answers to three decimal places.) and when I put in -2.186 its wrong.
 
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chapsticks said:

Homework Statement



arctan(8x-8)=-1

Homework Equations



I'm sure what this part wants.

The Attempt at a Solution



tan[arctan(8x-8)]=tan(-1)
8x-8=tan(-1)
x=(1/8)(tan(-1)+8)
x=(1/8)(-(tan(1)+8)
x=

I am stuck on the last part since the homework says Simplify the above equation. (Round your answers to three decimal places.) and when I put in -2.186 its wrong.

Your working is right. I initially thought you were putting the calculator in degrees, but that's not it. You must be doing something else wrong to get that wrong value.

Anyway, put your calculator into radians (RAD) mode and work that out again. Pay attention to where all the brackets are, better still work out what 8 - tan(1) is first, then divide by 8.
 
I do not get (1/8)(-tan(1)+8) to be equal to -2.186. How did you get that? What's tan(1)?
 
sorry I just realized that it was for a different problem my answer for this was .805
 
chapsticks said:
sorry I just realized that it was for a different problem my answer for this was .805

Right answer.
 

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