F4 09 Trigonometry Ii
- 1. ppr maths nbk CHAPTER 9: TRIGONOMETRY II EXERCISE 1 1. In Diagram 1, ABC is a straight line. D 6 cm 10 cm xo A B C DIAGRAM 1 Find the value of sin xº. 2. In Diagram 2, ABC is a straight line. D 5 cm 13 cm yo A B C DIAGRAM 2 Find the value of cos yº. 3. Find the value of tan 0o + 2 sin 90o – 3 (cos 180o). 4. Diagram 3 shows the curve y = f(x)? 1 y=f(x) 0 90 180 270 360 -1 DIAGRAM 3 State the name of the curve y = f(x). 94
- 2. ppr maths nbk 5. State the angle in the first quadrant that is equivalent to 200º. 6. In Diagram 4, BCD is a straight line. A 7 cm 5 cm 3 cm θ B C D DIAGRAM 4 Find tan θ. 7. In Diagram 5, BCD is a straight line. A 2 cm θ B 2 cm C 2 cm D DIAGRAM 5 Find cos θ. 8. In Diagram 6, ABC is a right angled-tringle. A B 25cm θ C DIAGRAM 6 4 Given that sin θ = , find the length of BC 5 95
- 3. ppr maths nbk 9. In Diagram 7, BDC is a straight line. A 10 cm x y B D C DIAGRAM 7 3 4 Given that sin x = and tan y = , find, the length, in cm, of BC. 5 5 10. In diagram 8, BCD is a straight line. A 16 cm x y 20 cm B C D DIAGRAM 8 Given that cos y = 0.6, find the value of cos x. 96
- 4. ppr maths nbk CHAPTER 9: TRIGONOMETRY II EXERCISE 2 1. 1 In Diagram 1, PQR is a straight line and PQ = QR 3 S 8 cm xo P 5 cm Q R Find the value of sin xo. Answer: ……………………………….. 2. In Diagram 2, PQR is a straight line. R Q 6 cm P 8 cm S DIAGRAM 2 Find the length of QS, in cm. Answer : …………………………………. 3. Given that tan θ = 0.7382 and 180o ≤ θ ≤ 360o, find the value of θ. Answer : ……………………….……… 97
- 5. ppr maths nbk 4. In Diagram 3, O is the centre of a unit circle. y 1 (-0.8,0.6) xo x -1 O 1 -1 DIAGRAM 3 Find the value of tan xo. Answer: …………………………….. 5. In Diagram 4, PQRS is a rectangle. P Q x° 10 cm M S 12 cm R DIAGRAM 4 Find the value of cos xo. Answer : ……………………………… 98
- 6. ppr maths nbk 6. Diagram 5 shows the graph of y = cos xo. y 1 p O x -0.5 -1 DIAGRAM 5 Determine the value of p . Answer : ……………………………. 7. In Diagram 6, PTU and PQRS are straight lines. U T 17 cm x° P Q R S 15 cm DIAGRAM 6 o Find the value of cos x . Answer : …………………………… 8. In Diagram 7, PQR is a straight line. S 12 cm x° P Q R DIAGRAM 7 4 It is given that cos x o = − . Find the length of SP, in cm. 5 Answer : …………………………. 99
- 7. ppr maths nbk 9. In Diagram 8, PRS is a straight line and RS = 12 cm. T 25 cm 15 cm x° P R S 15 cm Q DIAGRAM 8 Find the value of sin xo. Answer : …………………………….. 10. In Diagram 9, QRST is a straight line. P 17 cm 8 cm x° Q R S T 21 cm DIAGRAM 9 Find the value of sin xo. Answer : …………………………….. 100
- 8. ppr maths nbk CHAPTER 9: TRIGONOMETRY II DIAGNOSTIC TEST 3 1. Given that, sin θ = and 90 o ≤ θ ≤ 180 o , find the value of cos θ . 5 4 A 5 5 B 3 4 C − 5 3 D − 4 2. Determine the equivalent of sin 46o 24’ . A cos 133o 36’ B sin 133o 36’ C sin 226o 24’ D sin 313o 36’ 3. Given that, cos 45o = 0.7071. Find the value of cos 225o A -0.7071 B -0.6929 C 0.6929 D 0.7071 4. In Diagram 1, BCD is a straight line. Find the value of cos ro. ro B 4 cm A C 3 cm D DIAGRAM 1 4 A − 5 3 B 5 3 C − 5 3 D − 4 101
- 9. ppr maths nbk 5. By using a calculator, find the value of cos 216o 24’ A 0.8048 B 0.8049 C -0.8049 D -0.8048 6. In Diagram 6, PQR is a straight line and PR = 10 cm. P x° Q S R 12 cm DIAGRAM 6 Find the value of cos xo. 5 A − 13 12 B − 13 5 C 13 12 D 13 102
- 10. ppr maths nbk 7. 3 In Diagram 7, PRS is a straight line and tan x = . 4 S y° R T 6 cm 5 cm x° P Q DIAGRAM 7 Find the value of tan yo. 1 A − 2 5 B − 8 1 C 2 5 D 8 8. Which of the following graphs represents y = cos x ? A B y y 1 1 O 180 x O 90 180 90 -1 -1 C D y y 1 1 O x 90 180 90 180 O -1 -1 103
- 11. ppr maths nbk 9. In Diagram 9, O is the centre of a unit circle. y x° O x (0.5,-0.866) DIAGRAM 9 o Determine the value of sin x . A 0.5 B -0.866 C -1.732 D -0.5774 10. Given that cos x = cos 110o and 180o ≤ x ≤ 360o, find the value of x. A 200o B 250o C 290o D 340o 104