II. Solve for the value of $$ x $$ using a scientific calculator and round of your answer to whole Uumber. $$ \begin{array}{ll}\tan x=\frac{16}{21} \ \text { SOLION: } \ \tan x=\frac{16}{21} \ x=\tan ^{-1}\left(\frac{16}{21}\right) & \rightarrow \text { dake the inverse of tan. This is usually labeled as tan } 16 \text { by } 21 \text { to get atan the decimal form } 0.7619\end{array} $$ $$ \begin{array}{ll}x=\tan ^{-1}(0.7619) \rightarrow \text { type this on your scientfic calculator and round aff your answer to whole number } \ \text { 1. } \cos x=\frac{4}{5} & \text { 14. } \sin x=\frac{12}{17}\end{array} $$ $$ \begin{array}{ll}\text { 2. } \sin x=\frac{2}{5} & \text { 15. } \tan x=\frac{13}{25} \ \text { 3. } \tan x=\frac{7}{5} & \text { 16. } \cos x=\frac{8}{15}\end{array} $$

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UpStudy AI · Accepted Answer

To solve for the value of $$ x $$ given the equation $$ \tan x = \frac{16}{21} $$, we will follow these steps:

1. **Use the inverse tangent function**: We need to find $$ x $$ by taking the inverse tangent (arctan) of $$ \frac{16}{21} $$.
2. **Calculate the value**: Use a scientific calculator to compute $$ x = \tan^{-1}\left(\frac{16}{21}\right) $$.
3. **Round the answer**: Finally, round the result to the nearest whole number.

Let's perform the calculation for $$ x $$:

$$
x = \tan^{-1}\left(\frac{16}{21}\right)
$$

Now, I will calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$\arctan\left(\frac{16}{21}\right)$$
The calculation gives us:

$$
x = \tan^{-1}\left(\frac{16}{21}\right) \approx 0.651077
$$

Now, we will round this value to the nearest whole number. Since $$ 0.651077 $$ is less than $$ 1 $$, rounding it gives us:

$$
x \approx 1
$$

Thus, the final answer is:

$$
\boxed{1}
$$
$$ x = 1 $$

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