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Home > PC > Chapter 6 > Lesson 6.1.2 > Problem 6-28

6-28.
  1. Sylvie needs to solve cos x = −0.3 on a math test. She knows that cos−1 is the inverse function for cosine, so she applies this function to both sides of the equation. This gives her x = cos−1(− 0.3) ≈ 1.875. But when her test is returned, she finds she earned only partial credit on the problem. Homework Help ✎

    1. What is wrong with Sylvie’s method?

    2. What should Sylvie have answered to receive full credit? Explain your answer.

There are multiple solutions.

Sylvie needs to include all the solutions, which she can get using a graph or unit circle.
She needs to add multiples of 2π, and include the negative values. x = ±1.875 + 2πn ,where n is an integer.