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Answer :
Let's go through the steps to order the expressions [tex]\(\sin A = \tan A\)[/tex], [tex]\(\cos A\)[/tex], and [tex]\(\tan C\)[/tex] from least to greatest:
1. Determine the Values:
- We are given [tex]\(\cos A = \frac{24}{40}\)[/tex].
- We are given [tex]\(\tan C\)[/tex] as both [tex]\(\frac{2y}{30}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex]. Using [tex]\(\tan C = \frac{32}{40}\)[/tex] as it is a complete expression.
- We are given [tex]\(\sin A = \frac{32}{42}\)[/tex] and it is stated that [tex]\(\sin A = \tan A\)[/tex]. So, [tex]\(\tan A = \frac{32}{42}\)[/tex].
2. Calculate Numerical Values:
- Calculate [tex]\(\cos A\)[/tex]:
[tex]\[
\cos A = \frac{24}{40} = 0.6
\][/tex]
- Calculate [tex]\(\tan C\)[/tex]:
[tex]\[
\tan C = \frac{32}{40} = 0.8
\][/tex]
- Calculate [tex]\(\tan A\)[/tex] (which is [tex]\(\sin A\)[/tex]):
[tex]\[
\tan A = \frac{32}{42} \approx 0.7619
\][/tex]
3. Order from Least to Greatest:
- Now, we have the values:
- [tex]\(\tan A \approx 0.7619\)[/tex]
- [tex]\(\cos A = 0.6\)[/tex]
- [tex]\(\tan C = 0.8\)[/tex]
- Arranging these in order from least to greatest:
[tex]\[
0.6, \; 0.7619, \; 0.8
\][/tex]
4. Conclusion:
- Therefore, the order of the values from least to greatest is:
[tex]\[
\cos A, \; \tan A, \; \tan C
\][/tex]
So, the expressions in order from least to greatest are: [tex]\(\cos A\)[/tex], [tex]\(\tan A\)[/tex], [tex]\(\tan C\)[/tex].
1. Determine the Values:
- We are given [tex]\(\cos A = \frac{24}{40}\)[/tex].
- We are given [tex]\(\tan C\)[/tex] as both [tex]\(\frac{2y}{30}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex]. Using [tex]\(\tan C = \frac{32}{40}\)[/tex] as it is a complete expression.
- We are given [tex]\(\sin A = \frac{32}{42}\)[/tex] and it is stated that [tex]\(\sin A = \tan A\)[/tex]. So, [tex]\(\tan A = \frac{32}{42}\)[/tex].
2. Calculate Numerical Values:
- Calculate [tex]\(\cos A\)[/tex]:
[tex]\[
\cos A = \frac{24}{40} = 0.6
\][/tex]
- Calculate [tex]\(\tan C\)[/tex]:
[tex]\[
\tan C = \frac{32}{40} = 0.8
\][/tex]
- Calculate [tex]\(\tan A\)[/tex] (which is [tex]\(\sin A\)[/tex]):
[tex]\[
\tan A = \frac{32}{42} \approx 0.7619
\][/tex]
3. Order from Least to Greatest:
- Now, we have the values:
- [tex]\(\tan A \approx 0.7619\)[/tex]
- [tex]\(\cos A = 0.6\)[/tex]
- [tex]\(\tan C = 0.8\)[/tex]
- Arranging these in order from least to greatest:
[tex]\[
0.6, \; 0.7619, \; 0.8
\][/tex]
4. Conclusion:
- Therefore, the order of the values from least to greatest is:
[tex]\[
\cos A, \; \tan A, \; \tan C
\][/tex]
So, the expressions in order from least to greatest are: [tex]\(\cos A\)[/tex], [tex]\(\tan A\)[/tex], [tex]\(\tan C\)[/tex].
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