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If cos x=1/2, then what is the positive value of sin(1/2)x, in simplest radical form with a rational denominator?

User Dstandish
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Final answer:

Given that cos x = 1/2, sin(1/2)x is equivalent to sin(π/6). The value of sin(π/6) = 1/2, which does not involve a radical and is already in its simplest form.

Step-by-step explanation:

Given that cos x = 1/2, we want to find the positive value of sin(1/2)x in simplest radical form with a rational denominator. To do this, we first identify the angle whose cosine is 1/2. The angles with this property are x = π/3 and x = 5π/3 radians (or x = 60° and x = 300° degrees) in standard trigonometric positions. However, since we are looking for a positive value and considering the fundamental trigonometric identities, we'll use x = π/3.

Since sin(1/2)x = sin(1/2)(π/3) = sin(π/6), we can then refer to the known value of sin(π/6) = 1/2. The value of sin(π/6) is already in its simplest radical form, as it does not involve a radical. Therefore, sin(1/2)x = sin(π/6) = 1/2.

User Batista
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