Revision as of 09:21, 22 December 2023 edit AnonymousMathsFan2520 (talk \| contribs) 10 edits Error of the approximation Tag: Visual edit ← Previous edit		Revision as of 11:10, 22 December 2023 edit undo AnonymousMathsFan2520 (talk \| contribs) 10 edits Undid my previous edit in Error of the approximations. Tag: Visual edit Next edit →
Line 77: * {{math\|sin ''θ'' ≈ ''θ''}} at about 0.2441 radians (13.99°) * {{math\|cos ''θ'' ≈ 1 − {{sfrac\|''θ''<sup>2</sup>\|2}}}} at about 0.6620 radians (37.93°) The error can be compared using the Maclaurin Series. Since the next smallest degree of x that is not included in the cos(x) approximation is 2, for the sin(x) approximation it is 3 and for the better cos(x) approximation it is 4, it can easily be seen that the cos(x) approximation is accurate for less than the sin(x) approximation which is accurate for less than the better cos(x) approximation. == Angle sum and difference == The [[angle addition and subtraction theorems]] reduce to the following when one of the angles is small (''β'' ≈ 0):

Small-angle approximation: Difference between revisions