Respuesta :
Answer:
To sketch the angle in standard position, we can use the coordinates (9.3, 8.6) to plot the point in the Cartesian plane. The angle is measured counterclockwise from the positive x-axis.
Now, let's calculate the distance \( r \) from the origin to the point (9.3, 8.6) using the distance formula:
\[ r = \sqrt{(x^2 + y^2)} \]
\[ r = \sqrt{(9.3^2 + 8.6^2)} \]
\[ r \approx \sqrt{(86.49 + 73.96)} \]
\[ r \approx \sqrt{160.45} \]
\[ r \approx 12.66 \]
Now, let's find the trigonometric ratios:
1. \( \sin A = \frac{y}{r} \)
\[ \sin A = \frac{8.6}{12.66} \]
\[ \sin A \approx 0.678 \]
2. \( \cos A = \frac{x}{r} \)
\[ \cos A = \frac{9.3}{12.66} \]
\[ \cos A \approx 0.735 \]
3. \( \tan A = \frac{y}{x} \)
\[ \tan A = \frac{8.6}{9.3} \]
\[ \tan A \approx 0.925 \]
So, summarizing the results to 3 significant digits:
- \( r \approx 12.7 \)
- \( \sin A \approx 0.678 \)
- \( \cos A \approx 0.735 \)
- \( \tan A \approx 0.925 \)
