Answer:
- using y = x, the error is about 0.1812
- using y = (x -Ο/4 +1)/β2, the error is about 0.02620
Step-by-step explanation:
The actual value of sin(Ο/3) is (β3)/2 β 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=Ο/3 is ...
... x -sin(x) @ x=Ο/3
... Ο/3 -(β3)/2 β 0.18117215 β 0.1812
You know right away this is a bad approximation, because the approximate value is Ο/3 β 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-Ο/4)/β2 (no error at x=Ο/4), then the error at x=Ο/3 is ...
... (x+1-Ο/4)/β2 -sin(x) @ x=Ο/3
... (Ο/12 +1)/β2 -(β3)/2 β 0.026201500 β 0.02620
