Page 162 - ADVANCED MATH F.5

Form Five Form Five

Derivatives of trigonometric functions
Teaching steps

1. Guide students through discussion to identify trigonometric
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functions that involve sine, cosine, tangent, secant, cosecant,
and cotangent with their units in radians.
2. Design a strategy which will engage students to deduce the
derivatives of sine, cosine, and tangent from first principles.
3. Use Examples 8.21 to 8.26 in the Student’s Book to guide
students through discussion to differentiate trigonometric
functions. Allow students to share alternative methods of
differentiating trigonometric functions. Engage them to use
mathematical software to verify the solutions of the given
Examples.

4. Instruct students to attempt Exercise 8.8 in the Student’s Book.
Advise students to submit their work; check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 8.8

1. (a) 2cos2x (b) 2 sinx xx+ 2 cos x

2
2 ⎛⎞
(c) − cos ⎜⎟ (d) 12sin 2x−
x 2 ⎝⎠
x
1
2
(e) 2 sin 1x ( − x (f) − x 4 ( sinx x + 3cos ) x
)

(g) cos x + cos2x (h) x + 2 sec 2 ( x + 2 )
2(x + 2)

) (3x −
(i) 4sec 4x (j) 12 cos 3x ( x − 2 1 sin 2 ) 1
2

156
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