Use a calculator to evaluate each expression to the nearest tenth of a degree.

Question

Use a calculator to evaluate each expression to the nearest tenth of a degree. $$ \sin ^{-1}(0.6498)= $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\arcsin\left(0.6498\right)$$
Calculate or simplify the expression $$ 0.707321 * \frac{180}{\pi} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.707321\times \frac{180}{\pi }$$
- step1: Convert the expressions:
  $$\frac{707321}{1000000}\times \frac{180}{\pi }$$
- step2: Multiply the numbers:
  $$\frac{6365889}{50000\pi }$$
To evaluate $$ \sin^{-1}(0.6498) $$:

1. First, we find the arcsine of $$ 0.6498 $$:
   $$
   \arcsin(0.6498) \approx 0.707321 \text{ radians}
   $$

2. Next, we convert radians to degrees using the conversion factor $$ \frac{180}{\pi} $$:
   $$
   0.707321 \times \frac{180}{\pi} \approx 40.526508 \text{ degrees}
   $$

3. Rounding to the nearest tenth of a degree:
   $$
   \approx 40.5^{\circ}
   $$

Thus, $$ \sin^{-1}(0.6498) \approx 40.5^{\circ} $$.
$$ \sin^{-1}(0.6498) \approx 40.5^{\circ} $$

Use a calculator to evaluate each expression to the nearest tenth of a degree.

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