7.2  Remarks

1. The approximations derived above are valid only when q is measured in radians.

    

2. These approximations are valid to about 3 significant figures for angles in the range
-0.114 rad < q < 0.114 rad    or
-6.53° < q < 6.53°.
q =          1 - ½ q² = 

sin q =      tan q =      cos q = 

 

3. If q is small, multiples of q are also considered small.

i.e.     sin 2q	» 2q
cos 3q	» 1 - ½(3q)2
tan ½q	» ½q, ¼ etc

But sin (q + p/6) is not approx (q + p/6).

 

4. Sine and cosine rule formulae are sometimes useful in solving problems on small angles and approximations.

Sine rule:

a ¾¾ sin A

=

b ¾¾ sin B

=

c ¾¾ sin C

Cosine rule:
 

a2 = b2 + c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B c2 = a2 + b2 - 2ab cos C

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