Michigan State University - Diagnostic Exam

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6.10

  •   The solution(s) of the equation sin2 x + cosx = 1 with 0≤ x < 2π satisfy which of the following?

    a) There is 1 solution b) There are 2 solutions
      
    c) There are 3 solutions d) There are 4 solutions
      
    e) There are no solutions

Solution:

2 2 sin x + cosx = 1 ⇒ (1 - cos x) + cos x = 1 ⇒ cos x(1 - cos x) = 0 ⇒ cos x = 0 or cos x = 1

It follows that

cos x = 0 ⇒ x = π-, 3π 2 2 cos x = 1 ⇒ x = 0

Diagnostic:

If you miss this question please review Pythagorean Identities.

Also, see 5.10: Equations of Quadratic Type and 6.6: Trigonometric Equations .

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July 15, 2008