Question

Tg(2009arcsin(-arcsin(-√3/2))

Answer 1

$\arcsin(-\arcsin(-\frac{\sqrt{3}}{2}))=\arcsin(\arcsin\frac{\sqrt{3}}{2})=\arcsin\frac{\pi}{3}.$

Поскольку $\pi>3\Rightarrow \frac{\pi}{3}>1\Rightarrow \arcsin\frac{\pi}{3}$ не существует, поэтому $tg(2009\arcsin(-\arcsin(-\frac{\sqrt{3}}{2})))$ не существует

Answer 2

To simplify the given expression, let's start by evaluating the innermost operation first:

1. Evaluate -√3/2: -√3/2 ≈ -0.866

2. Next, take the inverse sine (arcsin) of -0.866: arcsin(-0.866) ≈ -60°

3. Now, take the negative of the result: -(-60°) = 60°

4. Finally, apply the tangent function (Tg) to 60°: Tg(60°) ≈ √3 ≈ 1.732

So, the simplified value of the expression Tg(2009arcsin(-arcsin(-√3/2))) is approximately 1.732.