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.) ?

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.

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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