Finding the Arctangent of an Unknown Number

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SUMMARY

The discussion focuses on finding the arctangent of an unknown number, specifically arctan(-2). It is established that while half-angle and double-angle formulas are not applicable, understanding the tangent function's graph is crucial. The tangent function includes asymptotes and a repeating pattern, while the arctangent function is a one-to-one function that does not repeat. Visualizing these functions aids in comprehending the relationship between angles and their tangent values.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent and arctangent.
  • Familiarity with the unit circle and angle measurements.
  • Basic graphing skills for visualizing functions.
  • Knowledge of asymptotes and periodic functions in trigonometry.
NEXT STEPS
  • Study the properties of the arctangent function and its graph.
  • Learn how to use a scientific calculator to compute arctan values.
  • Explore the relationship between trigonometric functions and their inverses.
  • Investigate the applications of arctangent in real-world problems, such as in physics and engineering.
USEFUL FOR

Students, educators, and anyone interested in mastering trigonometric functions, particularly those looking to understand the arctangent and its applications in mathematics.

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How do you go about finding the arctangent of an unfamiliar number. Example, arctan (-2)? I think it's in the direction of half-angles and double angels, but how do I get the angle to start with the formulas in the first place?

Thanks in advance!
 
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If x = arctan(-2), then tan(x) = -2. I don't think double or half-angle will help you for this problem. Sometimes you can figure out what x is, sometimes you can't without a calculator.
 
xXOfNiRXx said:
How do you go about finding the arctangent of an unfamiliar number. Example, arctan (-2)? I think it's in the direction of half-angles and double angels, but how do I get the angle to start with the formulas in the first place?

Thanks in advance!

I like to visualize the plots of sin, cos, and tan, to help me with problems like this. Draw the tan function, including the asymptotes and the repeating pattern. The arctan is just that plot turned on its side, but without the repeating patterns (because that would give you multiple values for arctan).

http://en.wikipedia.org/wiki/Arctan

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