If tan 1

Question

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x = f, what is sin x in terms of f

Answer 1

Using the trigonometric identity for tangent, we have:

tan(1/2 x) = f

Since tan(1/2 x) = sin(1/2 x) / cos(1/2 x), we can rewrite the equation as:

sin(1/2 x) / cos(1/2 x) = f

Multiplying both sides by cos(1/2 x) to isolate sin(1/2 x), we get:

sin(1/2 x) = f * cos(1/2 x)

Since sin x = 2 * sin(1/2 x) * cos(1/2 x), we can plug in our expression for sin(1/2 x) to get:

sin x = 2 * (f * cos(1/2 x)) * cos(1/2 x)

Therefore, sin x in terms of f is:

sin x = 2f * cos^2(1/2 x)