How do I determine all the possible solutions for the equation sin(2x) = cos(x) within one period in radians?
Answer 1
Michelle Diaz
To find all solutions for sin(2x) = cos(x) within one period [0, 2π), use the identity sin(2x) = 2sin(x)cos(x). This converts the equation to 2sin(x)cos(x) = cos(x). Solving, we get cos(x)(2sin(x) – 1) = 0. The solutions are x = π/2, 3π/2, and x = π/6, 5π/6.
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