Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Trigonometry Test REVISION Name: ___________________________ Section A Multiple Choice 1 Given sin = 0.4, then cos = A 0.7 B 0.9 C 0.6 D 0.4 E 0.5 B 2 cos 1322′53″ correct to four decimal places is: A 0.2311 B 0.2312 C 0.9734 D 0.9735 E 0.9729 E tan 13cos 82 = A 0.37 B 0.44 C 1.4 D 0.032 E 0.97 D 3 4 The size of the angle, a, in the figure below is: 5 A B C D E 6 C 4244′25″ 4215′13″ 4744′47″ 3355′3″ 4755′33″ MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION C 50.3 25.4 28.5 50.1 113 The size of the angle, d, in the figure below is: A B C D E A 98.3 63.4 181.5 63.5 89.3 The length of the side, c, in the figure below is: A B C D E 7 A B C D E The length of the side, b, in the figure below is: 2618′42″ 6341′18″ 4152′23″ 487′37″ 6814′15″ B 8 The size of the angle, e, in the figure below is: A B C D E B 12 A hiker travels for 9.8 km on a bearing 082T. The distance the hiker is north of the starting point is: A 7.9 km B 9.7 km C 1.4 km D 4.9 km E 9.4 km 432' 4658' 5541' 3418' 469' 9 A tree 34 m high casts a shadow 12 m A long. The angle of inclination of the sun is closest to: A 70 B 21 C 69 D 19 E 79 10 A chord of a circle subtends an angle of E 15 at the centre. If the chord is 13 cm long, then the radius of the circle is closest to: A 100 cm B 104 cm C 39 cm D 52 cm E 50 cm 11 The true bearing of N75W is: A 075T B 255T C 105T D 285T E 345T D MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION C Trigonometry Test REVISION Name: ___________________________ Section B Short/Extended answer 1 Find the angle for each of the following in degrees, minutes and seconds. (a) cos = 0.8 (b) 2 tan = 10.6732 Find the length of the side, f, in the figure below. 4 (a) cos = 0.8 cos 1 0.8 365212 (b) tan = 10.6732 tan 1 10.6732 843851 A H f cos 30 17.2 f 17.2 cos 30 cos 3 f 14.9 3 Find the length of the side, g, in the figure below. O H 2.14 sin 166' g 2.14 g sin 166' sin 3 g 7.72 4 Find the size of the angle, h, in the figure below, correct to the nearest minute. O A 15.1 tan h 14.7 tan 15.1 14.7 h 4546' h tan 1 MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION 3 5 Find the length of the side, i, in the figure below. sin 3 O H i 27.12 i 27.12 sin 2712' sin 2712' i 12.40 6 Find the length of the side, j, in the figure below. A H 1046 cos 2417' j 1046 j cos 2417' cos 3 j 1148 7 Find the length of the side, k, in the figure below. O A k tan 571' 2.36 k 2.36 tan 571' tan 3 k 3.64 8 From the top of a building, 202 m high, the angle of depression to another building, 120 m away, is 25. How high is this second building? 4 O A x tan 25 120 x 120 tan 25 tan x 55.96 Height of 2nd building h h 202 55.96 h 146.04 h 146 m MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION 9 The diameter of a vertical cone is 7.5 cm and its semi-vertical angle is 27. Calculate the length of the slant edge of the cone. 4 Right-angled triangle constructed by halving diameter. O sin H 3.75 sin 27 l 3.75 l sin 27 l 8.26 cm 10 Change the following true bearings to compass bearings: (a) 193T (a) (b) 272T (b) 4 180 + 13 = 193 193T = S13W 360 – 272 = 88 272T = N88W MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION 11 A plane flies for 195 km on a bearing of 10211'T and then for 104 km on a bearing 21322'T How far south of the starting point is the plane? 5 First leg of journey. opposite sin hypotenuse s sin 1211' 1 195 s1 195 sin 1211' s1 41.15 Second leg of journey. adjacent cos hypotenuse s cos 3322' 2 104 s 2 104 cos 3322' s 2 86.86 Distance south of starting point s1 s 2 41.15 86.86 128 .01 128 km MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION 12 13 14 If sin = 0.0305: (a) What is the angle (to the nearest minute)? (a) sin = 0.0305 sin 1 0.0305 145' (b) What is the value of cos ? (b) cos cos145' cos145' 0.9995 (c) Calculate tan . (c) tan tan 145' tan 145' 0.0306 (d) Show this information on a well labelled diagram. (d) State in which quadrant each of the following angles lies. (a) 192 (a) 192 is in 3rd quadrant as 180 192 270 (b) (b) 172 is in 2nd quadrant as 90 172 180 172 6 2 Calculate sin 65 and compare this answer with sin 65 = 0.9063 each of the following. What can you conclude? (a) sin 115 (a) sin 115= 0.9063 Therefore sin 115 = sin 65 (b) sin 245 (b) sin 245 = 0.9063 Therefore sin 245 = –sin 65 (c) sin 295 (c) sin 295 = 0.9063 Therefore sin 295 = sin 65 MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION 4 15 Complete the table of values for the rule y = sin x and use the range of x values given to sketch the graph. x 0° 30° 60° 90° 120° 150° 180° y x 210° 240° 270° 300° 330° 360° 390° y 16 (a) Convert 120º to radian measure, expressing the answer in terms of π. 5 Convert the radian measurement to 6 degrees. 4 x 0° 30° 60° y 0 0.5 0.9 1 0.9 0.5 0 x 210° 240° 270° 300° 330° 360° 390° y –0.5 –0.9 (a) 120º = (b) 5 6 c (b) 90° 120° 150° 180° MathsQUEST Chapter 4 (A,B,C,D,E,F,G) - Trigonometry Test REVISION c –1 –0.9 –0.5 120 180 c 2 = 3 180 5 = 6 = 150º 0 0.5 4