TRIGONOMETRY (LIVE) 10 APRIL 2015 Challenge Question ...

[Pages:4]TRIGONOMETRY (LIVE) Lesson Description

In this lesson we discuss: Reduction of compound / double angles Identities

General Solution

Challenge Question

If 18? = determine the following in terms of . a.) 18? b.) 78?

Section A: Summary Notes and Examples

10 APRIL 2015

(4) (5)

Grade 11 Revision

NB: You need to know and understand all of your Grade 11 Trigonometry as this knowledge will be needed to answer Grade 12 questions.

The following identities are important for tackling Grade 12 Trigonometry:

Example 1:

1.

Simplify:

cos + 60 + cos - 60

2.

Simplify the following without using a calculator:

tan -60? cos -156? 294? 492?

Page 1

Section B: Practice Questions

Question 1

1.1 Show that cos 60? + - cos 60? - = 3

(5)

1.2 Hence, evaluate 105? + 15? without using a calculator.

(5)

Question 2

Prove that:

2.1

1- 2- = tan

(6)

2-

2.2

2 = -

(5)

1+ 2 +

Question 3

Determine the general solution of: sin2x + cosx = 0

Page 2

Section C: Solutions

Challenge Question

a.)

18? = = 1

2 = ? - ? 2 = 1? - ? 2 = 1 - ?

= 1 - ?

x2 r2 y2

1

t x2 12 t 2

18

x2 1 t2

x

x 1t2

diagram Pythagoras = 1 - ? 18? = 1-? = 1 - ?

1

(4)

1 - ? 18? = 1 = 1 - ?

b.)

78?

= (60? + 18?)

= 60?. 18? + 60?. 18?

3

1

= 2 1 - ? + 2

3 1 - ?

=

2

+2

3 1 - 2 +

=

2

Practice Questions

(60? + 18?)

60?. 18? + 60?. 18?

3 and 1

2

2

1 - ? and

3 1 - ? + 1

2

2

(5)

Question 1

1.1

60? + - (60? - )

= 60?. - 60?. - ( 60? . + 60?. )

1

3

1

3

= 2 . - 2 . - 2 . - 2 .

= - 3

60?. - 60?.

cos 60?. + sin 60?.

3

2

1

2

- 3

(5)

Page 3

1.2

105? + 15?

= 60? + 45 - (60? - 45?)

= - 3 45?

2 =- 3 2

- 6 =2

Question 2

2.1

1 - 2 -

sin 2 - cos

1 - 1 - 2 2 - sin = 2 -

1 - 1 + 2 ? - = 2 -

2 ? - = 2 -

(2 - 1) = 92 - 1)

=

=

2.2

cos 2

1 + sin 2

? - ? = 1 + 2

( + )( - ) = ? + ? + 2

( + )( - ) = ? + 2 + ?

( + )( - ) = ( + ) + )

- = +

Question 3

Sin2x+cosx=0 2sinx.cosx+cosx=0 Cosx(2sinx+1)=0 Cosx=0 x=?90 +k.360

or sinx=-0.5 x= 210+k.360

Page 4

60? + 45 (60? - 45? - 3 45? 2

2

- 6

2

(5)

1 - 2 2 2 (2 - 1) (2 - 1) = sin

cos

(6)

? - ? 2 ( + )( - ) ( + )( + ) -

+

(5)

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