Ask Question
27 September, 08:25

What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = / pi/3? your answer should have at least three significant figures, accurate to within 0.1%. (e. g., 1.23 and 3.33e-8 both have three significant figures.) ?

+2
Answers (1)
  1. 27 September, 08:42
    0
    Answer: using y = x, the error is about 0.1812 using y = (x - π/4 + 1) / √2, the error is about 0.02620 Step-by-step explanation:

    The actual value of sin (π/3) is (√3) / 2 ≈ 0.86602540.

    If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

    ... x - sin (x) @ x=π/3

    ... π/3 - (√3) / 2 ≈ 0.18117215 ≈ 0.1812

    You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

    ___

    If the sine function is approximated by y = (x+1-π/4) / √2 (no error at x=π/4), then the error at x=π/3 is ...

    ... (x+1-π/4) / √2 - sin (x) @ x=π/3

    ... (π/12 + 1) / √2 - (√3) / 2 ≈ 0.026201500 ≈ 0.02620
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = / pi/3? your answer should have at least ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers