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Answer :
To solve the expression [tex]\(625 \cdot \sec^2\left(\frac{13}{25}\right) \cdot 8\pi\)[/tex], we will break it down into manageable steps:
1. Identify the Components:
- We have a constant value: 625.
- We have another constant denominated by [tex]\(8\pi\)[/tex].
- The trigonometric element: [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
2. Trigonometric Calculation:
- The secant squared of an angle is the inverse of the cosine squared of that angle. Mathematically, [tex]\(\sec^2(\theta) = \frac{1}{\cos^2(\theta)}\)[/tex].
- For the given angle [tex]\(\frac{13}{25}\)[/tex], calculate [tex]\(\cos\left(\frac{13}{25}\right)\)[/tex] and then find the inverse to get [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
3. Calculate [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex]:
- After calculation, [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex] equals approximately 1.3278.
4. Combine All Parts:
- Multiply the constant value 625 by the calculated [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
- Then take the result and multiply by [tex]\(8\pi\)[/tex] to finalize the expression.
5. Final Result:
- The expression evaluates to approximately 20857.4585.
This process will give you the calculated result of the expression using trigonometric identities and arithmetic operations.
1. Identify the Components:
- We have a constant value: 625.
- We have another constant denominated by [tex]\(8\pi\)[/tex].
- The trigonometric element: [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
2. Trigonometric Calculation:
- The secant squared of an angle is the inverse of the cosine squared of that angle. Mathematically, [tex]\(\sec^2(\theta) = \frac{1}{\cos^2(\theta)}\)[/tex].
- For the given angle [tex]\(\frac{13}{25}\)[/tex], calculate [tex]\(\cos\left(\frac{13}{25}\right)\)[/tex] and then find the inverse to get [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
3. Calculate [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex]:
- After calculation, [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex] equals approximately 1.3278.
4. Combine All Parts:
- Multiply the constant value 625 by the calculated [tex]\(\sec^2\left(\frac{13}{25}\right)\)[/tex].
- Then take the result and multiply by [tex]\(8\pi\)[/tex] to finalize the expression.
5. Final Result:
- The expression evaluates to approximately 20857.4585.
This process will give you the calculated result of the expression using trigonometric identities and arithmetic operations.
Thank you for reading the article Simplify the following expression tex 625 cdot sec 2 left frac 13 25 right cdot 8 pi tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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