$\cos \frac{10}{7} \div \frac{5}{4}$
Answer (1)
Rewrite the division as multiplication: cos 7 10 ÷ 4 5 = cos 7 10 × 5 4 .
Simplify the expression: 5 4 cos 7 10 .
Calculate the cosine value: cos 7 10 ≈ 0.1417459 .
Multiply to get the final answer: 5 4 × 0.1417459 ≈ 0.1133967 .
Explanation
Understanding the Problem We are asked to evaluate the expression cos 7 10 ÷ 4 5 . This involves dividing the cosine of a fraction by another fraction.
Rewriting the Expression First, we can rewrite the division as multiplication by the reciprocal: cos 7 10 ÷ 4 5 = cos 7 10 × 5 4 .
Simplifying the Expression This simplifies to 5 4 cos 7 10 . Here, the argument 7 10 is in radians. We can approximate the value of cos 7 10 using a calculator.
Calculating the Cosine Using a calculator, we find that cos 7 10 ≈ 0.1417459 . Therefore, 5 4 cos 7 10 ≈ 5 4 × 0.1417459 ≈ 0.1133967 .
Final Answer Thus, the final answer is approximately 0.1133967.
Examples
Imagine you are designing a bridge and need to calculate the stress on a support beam. The stress depends on the cosine of an angle, and you need to divide that value by a fraction to get the correct measurement. This problem demonstrates how trigonometric functions and fractions are used in engineering calculations to ensure structures are safe and stable.
