Please could somebody explain how the expression involving &#x03B8;<!-- θ --> that

excluderho 2022-06-27 Answered
Please could somebody explain how the expression involving θ that
1 + sin θ 5 + 3 tan θ 4 cos θ
approximates to for small values of θ is 1 2 θ + 4 θ 2 ?
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Answers (2)

Cahokiavv
Answered 2022-06-28 Author has 31 answers
Just compute the first terms of the Taylor series of 1 + sin θ 5 + 3 tan θ 4 cos θ , and you will get 1 2 θ + 4 θ 2 .
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misurrosne
Answered 2022-06-29 Author has 3 answers
Approximate the numerator and denominator up to θ 2 terms and get
1 + θ + o ( θ 2 ) 1 + 3 θ + 2 θ 2 + o ( θ 2 ) = ( 1 + θ ) ( 1 3 θ + 7 θ 2 ) + o ( θ 2 ) = 1 2 θ + 4 θ 2 + o ( θ 2 ) .
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