1 of 8 0-day streak

Use local polynomial approximations for circular functions

Question 1 of 8

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The following item uses a local approximation about x=0

Let \(x\)=\(-\frac{1}{10}\ \mathrm{rad}\)

Use the local rule to calculate the value of \(\cos(x)\)

(a)1 mark

Which angle unit is required by the small-angle relationships?

Use degrees for the angle

Use radians for the angle

(b)1 mark

Decide whether the prescribed approximation is suitable here

The local approximation is suitable for this value of x

The local approximation is not suitable for this value of x

Which prescribed local rule matches \(\cos(x)\)?

\cos(x)\approx x

\cos(x)\approx -x

\cos(x)\approx 1-\frac{x^2}{2}

(d)1 mark

Give the exact value produced by the prescribed approximation

approximate value

Format: exact