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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 \(x\)=\(\frac{1}{40}\ \mathrm{rad}\)

Find the approximate value of \(\tan(x)\) at this argument

(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

Is this argument in a suitable range for the local approximation?

The local approximation is not suitable for this value of x

The local approximation is suitable for this value of x

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

\tan(x)\approx -x

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

\tan(x)\approx x

(d)1 mark

Give the exact value produced by the prescribed approximation

approximate value

Format: exact