How many solutions does the equation cos (6x) = 1/2 have on the interval (0, 2pi) ?

Question

Mathematics

Tessa Flynn

29 July, 02:49

How many solutions does the equation cos (6x) = 1/2 have on the interval (0, 2pi) ?

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Answers (1)

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Quentin Malone · Answer 1

Cos (6 x) = 1/2

6 x = 60° ⇒ x 1 = 10°

6 x = 300° ⇒ x 2 = 50°

6 x = 420° ⇒ x 3 = 70°

6 x = 660° ⇒ x 4 = 110°

x 5 = 130°, x 6 = 170°, x 7 = 190°, x 8 = 230°, x 9 = 250°,

x 10 = 290°, x 11 = 310°, x 12 = 350°

Answer: there are 12 solutions on the interval (0, 2π).