Express y = arccos x in terms of y

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SUMMARY

The discussion focuses on expressing the function y = arccos x in terms of y, specifically converting arcsin x in relation to y. The participants emphasize the importance of visualizing the functions involved, suggesting that plotting the graphs of arccos x and arcsin x clarifies their relationship. The constraints of the functions are defined as -1 ≤ x ≤ 1 for x and 0 ≤ y ≤ π for y, which are critical for understanding the domain and range of the functions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically arccosine and arcsine.
  • Familiarity with the concepts of function plotting and graph interpretation.
  • Knowledge of the domain and range of trigonometric functions.
  • Basic skills in algebraic manipulation of equations.
NEXT STEPS
  • Learn how to derive relationships between inverse trigonometric functions.
  • Explore the properties of the unit circle to understand arcsin and arccos functions.
  • Study the graphical representation of trigonometric functions and their inverses.
  • Investigate the implications of function transformations on the domain and range.
USEFUL FOR

Students studying trigonometry, educators teaching inverse functions, and anyone interested in understanding the relationships between trigonometric functions and their inverses.

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Homework Statement


Give that:

y = arccosx -1<= x <= 1 and 0 <= y =< pi

a) express arcsin xin terms of y


Homework Equations





The Attempt at a Solution


Well I am given arccos x and i need to convert to arcsin x ?

Thanks :)
 
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Hi thomas49th :smile:

Just plot the functions and all should become clear
 

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