Answer :
To determine the value of \(\cos 28^\circ\), we need to evaluate the cosine of 28 degrees and match it to one of the given choices.
1. Converting Degrees to Radians:
\(\cos\) function typically uses radians in mathematical computations. Therefore:
[tex]\[ 28^\circ = \frac{28 \times \pi}{180} = \frac{28\pi}{180} = \frac{14\pi}{90} = \frac{7\pi}{45} \text{ radians} \][/tex]
2. Evaluating \(\cos 28^\circ\):
Using the conversion, we calculate \(\cos 28^\circ\). From the calculations, we find:
[tex]\[ \cos 28^\circ \approx 0.882947592858927 \][/tex]
3. Rounding the Result:
Round the result to two decimal places:
[tex]\[ \cos 28^\circ \approx 0.88 \][/tex]
4. Matching the Result to Given Choices:
None of the fraction choices is directly calculated from \(\frac{8}{17}, \frac{8}{15}, \frac{15}{17}, \frac{15}{8}\).
5. Verifying Choices:
Let's evaluate each fraction to check their decimal equivalents:
- \( \frac{8}{17} \approx 0.47 \)
- \( \frac{8}{15} \approx 0.53 \)
- \( \frac{15}{17} \approx 0.88 \)
- \( \frac{15}{8} \approx 1.875 \)
Among these, the fraction \( \frac{15}{17} \) is the closest to the calculated cosine value 0.88.
Thus, the correct answer is:
[tex]\[ \boxed{\frac{15}{17}} \][/tex]
1. Converting Degrees to Radians:
\(\cos\) function typically uses radians in mathematical computations. Therefore:
[tex]\[ 28^\circ = \frac{28 \times \pi}{180} = \frac{28\pi}{180} = \frac{14\pi}{90} = \frac{7\pi}{45} \text{ radians} \][/tex]
2. Evaluating \(\cos 28^\circ\):
Using the conversion, we calculate \(\cos 28^\circ\). From the calculations, we find:
[tex]\[ \cos 28^\circ \approx 0.882947592858927 \][/tex]
3. Rounding the Result:
Round the result to two decimal places:
[tex]\[ \cos 28^\circ \approx 0.88 \][/tex]
4. Matching the Result to Given Choices:
None of the fraction choices is directly calculated from \(\frac{8}{17}, \frac{8}{15}, \frac{15}{17}, \frac{15}{8}\).
5. Verifying Choices:
Let's evaluate each fraction to check their decimal equivalents:
- \( \frac{8}{17} \approx 0.47 \)
- \( \frac{8}{15} \approx 0.53 \)
- \( \frac{15}{17} \approx 0.88 \)
- \( \frac{15}{8} \approx 1.875 \)
Among these, the fraction \( \frac{15}{17} \) is the closest to the calculated cosine value 0.88.
Thus, the correct answer is:
[tex]\[ \boxed{\frac{15}{17}} \][/tex]
