SM015 - 7.2 (Notes Solutions)

7.2 Compound Angles

Friday, July 10, 2020 3:14 PM

Learning Outcomes:

At the end of the lesson, students should be able to

(a) Express the formulae , & .

(b) Express the double-angle formulae.

(c) Express the half-angle formulae.

(d) Express the factor formulae.

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Compound Angle Formulae

Double Angle Formulae

Half Angle Formulae

Factor Formulae

Topic 7.2 Page 1

Compound Angle Formulae

Friday, May 29, 2020 5:03 PM

Topic 7.2 Page 2

Example 1

Friday, May 29, 2020 10:48 PM

If and where A and B are acute angle,
find the following without using calculator :
Solutions:

(a)

(b)

(c)

Topic 7.2 Page 3

Example 2 & 3

Friday, May 29, 2020 10:48 PM

Example 2
Simplify

Example 3
Without using calculator, find the exact value for
(a) (b)
Solutions:
(a)

(b)

Topic 7.2 Page 4

Double & Half Angle Formulae

Friday, May 29, 2020 5:03 PM

Double Angle Formulae

Consider for

Consider for

Consider for

Half Angle Formulae

Consider for

Consider for

Consider for

Topic 7.2 Page 5

Example 4

Friday, May 29, 2020 10:48 PM

Given that where A in the fourth quadrant, find the

following without using calculator:

Solution:
A in the fourth quadrant

a) b)

Since
Hence ,

Topic 7.2 Page 6

Example 5 & 6 .

Friday, May 29, 2020 10:48 PM

Example 5

Without using calculator, find the exact value of

Solution:

Example 6 .

Prove the identity
Solution:

Topic 7.2 Page 7

Factor Formulae

Friday, May 29, 2020 5:03 PM

By referring to compound angle formulae for sin & cos
----------------(1)
----------------(2)
----------------(3)
----------------(4)

Consider
Consider
Consider
Consider

Topic 7.2 Page 8

Example 7 & 8

Saturday, May 30, 2020 11:52 AM

Example 7 as the product of 2 trigonometric
Express
functions.

Solution:

Example 8 as the sum of 2 trigonometric functions.
Express

Solution:

Topic 7.2 Page 9

Example 9

Saturday, May 30, 2020 11:52 AM

Prove the following identites:
(a) .

Solution:

(b) .
Solution:

Topic 7.2 Page 10