Circular Functions: Sec-1(-rad(2))

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SUMMARY

The discussion centers on the evaluation of the function Sec-1(-rad(2)), where participants clarify the interpretation of the input argument. The term "rad" is debated, with suggestions that it may refer to either "-2 radians" or "radical(2)" (√2). The correct approach involves using the identity sec(x) = 1/cos(x) to find the inverse cosine of -1/2 or -√2/2, depending on the interpretation. The consensus emphasizes the importance of understanding the context of the argument in trigonometric functions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically secant and inverse secant.
  • Familiarity with radians and their conversion to degrees.
  • Knowledge of the unit circle and cosine values.
  • Ability to use a scientific calculator in radian mode.
NEXT STEPS
  • Study the properties of inverse trigonometric functions, focusing on asec and its domain.
  • Learn how to convert between radians and degrees effectively.
  • Explore the unit circle to understand cosine values for common angles.
  • Practice using a scientific calculator to evaluate trigonometric functions in radian mode.
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone seeking to deepen their understanding of inverse trigonometric functions and their applications.

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Sec-1(-rad(2))
 
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rebecca120 said:
Sec-1(-rad(2))

Please supply more context, like the question as asked.

The argument of \( \rm{asec} \) is just a number so I don't see what \( \rm{rad} \) is doing in your question.

CB
 
rebecca120 said:
Sec-1(-rad(2))
-rad(2)? Do you mean "- 2 radians"? Use the fact that sec(x)= 1/cos(x) and use a calculator (making sure it is in "radian" mode) to find cos^{-1}(-1/2).

Or do you mean "radical(2)" as in "\sqrt{2}"? \frac{1}{\sqrt{2}}= \frac{\sqrt{2}}{2} so find cos^{-1}\left(-\frac{\sqrt{2}}{2}\right). You shouldn't need a calculator for that.
 

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