Page 193 - ADVANCED MATH F.5

Form Five Form Five

Integration of trigonometric functions
Teaching steps

1. Guide students through discussion to share some common
trigonometric identities before introducing integration of
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trigonometric functions.
2. Assist students through discussion to find solutions of integrals
of the form:

(a) , or
where a and b are constants. Instruct students to use
Table 9.3 in the Student’s Book to identify factor
formulae and the corresponding integrals.
∫
n
n
n
n
(b) sin x dx ; or ∫ cos x dx sin x dx ; or ∫ cos x dx
∫
∫
n
(c) tan xdx or sec xdx
n
3. Formulate strategies for assisting students in groups to study
carefully Examples 9.31 to 9.39 in the Student’s Book. Allow
students to share alternative methods of solving integrals
of trigonometric functions. Engage students in group to use
mathematical software to verify the solutions of the integrals
in the examples.
4. Require students to attempt Exercise 9.7 in the Student’s Book.
Advise them to submit their work. Check the correctness
of their answers, and provide them constructive feedback.
Encourage students to explore additional resources, such as
online tutorials, Symbolab, Mathematica, or reference books,
to enrich their understanding and for further practice.

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Mathematics for Advanced Secondary Schools

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