Inverse Sine and Inverse Cosine Trigonometric Functions Questions

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Complete the following questions :

  • In your own words, what does it mean to solve begin mathsize 12px style cos theta equals bevelled 1 half end style ? What does it mean using coordinates on a unit circle? Graphically (using cos x) what does it mean?
  • In your own words, what does it mean to solve begin mathsize 12px style cos theta equals negative.6 end style ? Why can’t you use the unit circle? How would you solve it using a calculator? Graphically?
  • Why can’t we have the range of both the inverse sine and inverse cosine be [0,pi]? It certainly would be easier to remember!
  • In what sense can we say that the inverse sine function “undoes” the sine function? And the sine function “undoes” the inverse sine function? What conditions need to be met?
  • Are cos–1(x) and 1/cos(x) the same thing? Explain.
  • Explain how to use your calculator to find csc-1(-4). You do not need to calculate it.