WISKUNDE GRAAD 10 TAAK 1 ONDERSOEK Punte: 55

MATHEMATICS GRADE 10 TASK 1 INVESTIGATION Marks: 55

INSTRUKSIES:

1. Die taak moet ingehandig word op 2 Maart 2015.

2. Beantwoord al die vrae. 3. Slegs vrae wat in blou of swart ink

beantwoord word, sal nagesien word. Sketse mag in potlood gedoen word.

4. Jy mag 'n sakrekenaar gebruik. Maak seker dat jou sakrekenaar op D (Casio) of DEG (Sharp) gestel is.

5. Rond antwoorde af tot EEN desimale plek waar nodig, tensy anders vermeld.

6. Oneerlikheid sal gepenaliseer word. 7. Bestudeer die videos oor

trigonometrie:

INSTRUCTIONS:

1. This task must be handed in on 2 March 2015.

2. Answer all the questions. 3. Only questions answered in blue or black

ink, will be marked. Sketches may be done in pencil.

4. You may use a calculator. Make sure your calculator is set to D (Casio) or DEG (Sharp)

5. Round answers to ONE decimal place where necessary, unless stated otherwise.

6. Dishonesty will be penalised. 7. Study the trigonometry videos.

https://www.youtube.com/watch?v=Jsiy4TxgIME

https://www.youtube.com/watch?v=VRz2d5yedsg

Wanneer trigonometrie gebruik word, word slegs een spesifieke hoek binne-in 'n reghoekige driehoek (nie die 90° hoek nie) gebruik. Hierdie spesifieke hoek bepaal dan ook die benoeming van die sye van die driehoek. Die sye is ook baie belangrik om sinus, cosinus en tangens van daardie spesifieke hoeke te bepaal.

When trigonometry is used, only one specific angle within a right-angled triangle (not the 90° angle) is used. This specific angle determines therefor the naming of the sides of the triangle. The sides are also very important to determine sine, cosine and tangens of that specific angles.

Bestudeer die volgende terminologie: Aangrensende sy (adjacent) Teenoorstaande sy (opposite) Skuinssy (hypotenuse)

Consider the following terminology: Adjacent side Opposite side Hypotenuse side

VRAAG 1

QUESTION 1

1.1 Die volgende driehoek word gegee:

1.1 The following triangle is given:

1.1.1 Teken die driehoek oor en benoem dan elke sy met betrekking tot 𝐶.

1.1.1 Redraw the triangle and name every side with regard to 𝐶.

1.1.2 Gee nou die trigonometriese verhouding van sin 𝐶, cos  𝐶 en tan 𝐶 in terme van die sye (AB, AC en BC).

1.1.2 Hence give the trigonometric ratio of sin 𝐶, cos  𝐶 and tan 𝐶 in terms of the sides (AB, AC and BC).

(4)

1.2 Die volgende driehoek word gegee:

1.2 The following triangle is given:

1.2.1 Teken die driehoek oor en benoem dan elke sy met betrekking tot 𝐴.

1.2.1 Redraw the triangle and name every side with regard to 𝐴.

1.2.2 Gee nou die trigonometriese verhouding van sin𝐴, cos  𝐴 en tan𝐴 in terme van die sye (AB, AC en BC).

1.1.2 Hence give the trigonometric ratio of sin𝐴, cos  𝐴 and tan𝐴 in terms of the sides (AB, AC and BC).

(4)

[8]

C

A

B

C

A

B

VRAAG 2

QUESTION 2

Maak twee sketse van ∆𝐷𝐸𝐹 Driehoek 1: 𝐸 = 90°, 𝐷 = 60° en 𝐹 = 30°. Merk 𝐷 duidelik en benoem al die sye met betrekking tot 𝐷. Driehoek 2: 𝐷𝐸 = 4  𝑐𝑚, 𝐸𝐹 = 6,9  𝑐𝑚 en 𝐷𝐹 = 8  𝑐𝑚. Merk 𝐹 duidelik en benoem al die sye met betrekking tot 𝐹.

Make two sketches of ∆𝐷𝐸𝐹 Triangle 1: 𝐸 = 90°, 𝐷 = 60° and 𝐹 = 30°. Clearly label 𝐷 and name all the sides with regard to 𝐷. Triangle 2: 𝐷𝐸 = 4  𝑐𝑚, 𝐸𝐹 = 6,9  𝑐𝑚 and 𝐷𝐹 = 8  𝑐𝑚. Clearly label 𝐹 and name all the sides with regard to 𝐹.

(3)

2.1 Bereken die volgende (gee die antwoord as 'n breuk en ook as 'n desimale getal)

2.1 Calculate the following (give the answer as a fraction and also as a decimal number)

2.1.1

sin𝐷

2.1.2 cos𝐷

2.1.3 tan𝐷

2.1.4 sin𝐹

2.1.5 cos𝐹

2.1.6 tan𝐹

(6)

2.2 Bereken die volgende op jou sakrekenaar (gee die antwoord as 'n desimale getal)

2.2 Calculate the following with a calculator (give the answer as a decimal number)

2.2.1

sin 60°

2.2.2 cos 60°

2.2.3 tan 60°

2.2.4 sin 30°

2.2.5 cos 30°

2.2.6 tan 30°

(6)

2.3 Wat let jy op omtrent jou antwoorde in 2.1 en 2.2?

2.3 What do you notice about your answers in 2.1 and 2.2? (2)

2.4 Beskou sin 60° en cos 30°.

2.4 Consider sin 60° and cos 30°.

2.4.1 Wat let jy op?

2.4.1 What do you notice? (1)

24.2 Wat dink jy is die rede hiervoor? 2.4.2 What do you think is the reason

for this? (1)

[19]

VRAAG 3

QUESTION 3

Skets ∆𝐾𝐿𝑀 𝐾𝐿 = 1,7  𝑐𝑚, 𝐿𝑀 = 1  𝑐𝑚 en 𝐾𝑀 = 2  𝑐𝑚. 𝐿 = 90°, 𝑀 = 60° en 𝐾 = 30°. Merk 𝑀 duidelik en benoem al die sye met betrekking tot 𝑀.

Draw ∆𝐾𝐿𝑀 𝐾𝐿 = 1,7  𝑐𝑚, 𝐿𝑀 = 1  𝑐𝑚 and 𝐾𝑀 = 2  𝑐𝑚. 𝐿 = 90°, 𝑀 = 60° and 𝐾 = 30°. Clearly label 𝑀 and name all the sides with regard to 𝑀.

(3)

3.1 Bereken die volgende (gee die antwoord as 'n breuk en ook as 'n desimale getal)

3.1 Calculate the following (give the answer as a fraction and also as a decimal number)

3.1.1

sin𝑀

3.1.2 cos𝑀

3.1.3 tan𝑀

(3)

3.2 Bereken die volgende op jou sakrekenaar(gee die antwoord as 'n desimale getal)

3.2 Calculate the following with a calculator (give the answer as a decimal number)

3.2.1

sin 60°

3.2.2 cos 60°

3.2.3 tan 60°

(3)

3.3 Vergelyk nou jou antwoorde in 2.1 en 2.2 met jou antwoorde in 3.1. en 3.2. Wat is jou gevolgtrekking hieroor?

3.3 Compare your answers in 2.1 and 2.2 with your answers in 3.1 and 3.2. What conclusion can you draw about this? (2)

[11] VRAAG 4 QUESTION 4 4.1 Gegee ∆𝐴𝐵𝐶: 4.1 Given ∆𝐴𝐵𝐶:

Bereken Calculate: 4.1.1

𝐴𝐵

4.1.2 sin 𝐶

4.1.3 cos𝐶

4.1.4 tan 𝐶

(4)

C

A

B

a

c

12

14,15

4.2 Gegee ∆𝐾𝐿𝑀: 4.1 Given ∆𝐾𝐿𝑀:

Bereken Calculate: 4.2.1

𝐾𝐿

4.2.2 sin𝑀

4.2.3 cos𝑀

4.2.4 tan𝑀

(4)

4.3 Gegee ∆𝑃𝑄𝑅: 4.1 Given ∆𝑃𝑄𝑅:

Bereken Calculate: 4.3.1

𝑃𝑅

4.3.2 sin𝑅

4.2.3 cos𝑅

4.2.4 tan𝑅

(4)

4.5 Beantwoord die volgende vrae: 4.5 Answer the following questions: 4.5.1 Wat kan jy omtrent hierdie

driehoeke aflei?

4.5.1 What can you deduce about these triangles? (1)

4.5.2 Wat kan jy sê omtrent 𝐴, 𝐾, 𝑃 ?

4.5.2 What can you say about 𝐴, 𝐾, 𝑃 ? (1)

4.5.3 Wat is die meetkundige term vir

hierdie driehoeke?

4.5.3 What is the geometric term for these triangles? (1)

4.5.4 Hoe sal jy trigonometrie beskryf?

Waarvoor dink jy word dit gebruik? Skryf 'n kort paragraaf om trigonometrie te beskryf.

4.5.4 How would you describe trigonometry? What do you think it is used for? Write a short paragraph to describe trigonometry.

(2)

[17] /55/

L

K

M 3

3,54

Q R

P

5,8

3,62