Topic 2 Periodic Functions and Applications I

 trigonometry – definition and practical applications of the sin, cos and tan ratios  simple practical applications of the sine and cosine rules

Model Calculate the value of the pronumeral in each of the following: cos x = x = cos = 50  50’ X° 19 cm 12 cm

Page 33 Exercise 2.1

Find the perimeter of the figure below.

 Perimeter = = 221m

Page 36 Exercise 2.2 No. 1 – 6 Page 42 Exercise 2.4 No. 1, 3, Worked solution Ex 2.4 No. 6

The Sine Rule A a b B c C

Model Find x in the following 85  c = x 65  A B C b = 15

Example 11, page 46 (Modelling and Problem Solving) Jermaine sees the top of a sand dune at an angle of 16°. On walking 40m closer, she finds the angle of elevation increases to 22°. What is the height of the sand dune? 16°22° 40m h A C B D * If we knew the length of line DB, we could easily work out the height.

16°22° 40m h A C B D Consider triangle ABD 16° 6°6° 158° 40m d b a

16°22°A B D C h 105.5m

Page 46 Exercise 2.5 N0. 1, 2(b,c,d,e), 3, 4, 7-9

The Cosine Rule A a b B c C Similarly

Model Find the length of the unknown side in the triangle below:  A B C c = b= a

Model Find the size of the largest angle in the triangle below: A B C c = b= a=8 N.B. Largest angle is always opposite the largest side

Page 50 Exercise 2.6

Examples 15 & 16, page 51 & 52 Page 53 Exercise 2.7 No. 1(a,b,c,f), 2(a,b,c,f), 4, 7, Worked solution Ex 2.7 No. 13

3D Applications Example 17: page 56 - From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B.

Consider triangle ABM Angle BAM is a right angle

- From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B. Consider triangle ABM A M B 50° 2 Km Side AM, which is common to both triangles, can now be calculated

- From point A, a mountain point due north is at an elevation of 20°. From point B, 2Km east of A and on the same level as A, the bearing of the peak is N40°W. Find the height of the peak above A and B. Now consider triangle AMP A P M 20° 2 tan50

Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower?

Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower? 52° 25° 103° FH W 575m We need side WH (f) f w =

Example 18: page 57 John observes that the top of a transmission tower at bearing 038° is at an elevation of 12°. Mary is 575m due east of John and can see the tower on a bearing of 295°. What is the height of the tower? 12° T HW 249.4m We can now calculate tower height

Page 59 Exercise 2.8 Worked solution Ex 2.7 No. 13