Page 122 - ADVANCED MATH F.5

Form Five Form Five

Trigonometric equations of the form a cos θ + b sin θ = c
Teaching steps
1. Guide students through discussion to solve equations of the
form cosa θ sinb θ + = cby using -formulae . Assist them in
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using the double angle formulae to express sin 2θ and cos 2θ
in terms of tanθ .
2. Assist students through discussion to perform Activity 6.2 in
the Student’s Book on deducing the -formulaet for cosθ and
tanθ . Guide students through discussion to use Figure 6.4 in
the Student’s Book of the right-angled triangle to deduce the
t-formula for sin , cos , and tan .θ θ θ Advise students to share
their work with other groups for more inputs.
3. Use Examples 6.26, 6.27, and 6.28 in the Student’s Book to
guide students in applying the -formulaet to find solutions
of the given trigonometric equations. Engage students to use
mathematical software of their choice to verify the answers of
the given examples. Advise them to share their work through
presentation.
4. Guide students through discussion to express cosa θ sinb θ +
in the form cos(R θα− ) or R cos(θ α+ ). Assist them to find
the maximum and minimum values of trigonometric equations
of the form cosa θ sinb θ + = . c
5. Use Examples 6.29 and 6.30 to guide students to express
a cosθ sinb θ + in the form of cos(R θα+ ) or R cos(θα− )
and use them to solve the given problems.

6. Guide students through group discussion to express
a cosθ sinb θ + in the form R sin(θ α+ ) or R sin(θα− ).
Assist them to determine the maximum or minimum values of
trigonometric equations of the form cosa θ sinb θ + = . c
7. Use Examples 6.31 to 6.35 in the Student’s Book to find the
solutions of the given trigonometric problems. Engage students

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 116
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