Mathematics for IT

[Author Name(s), First M. Last, Omit Titles and Degrees]

Question One: Trigonometric Functions; Angles
(a)
(i) 7/sin 35=10/sin A
Sin A= (sin 35*10)/7
A=55⁰
(ii) s2 =72+102
s2=49+100
s2=149
s= √149=12.21 cm
(b) For a small Ɵ, a triangle as shown below is noticed
i. With a small value of Ɵ, the opposite angle i.e. a is very small with the adjacent angle i.e. b as
well as the hypotenuse (h) being relatively large. Hence,
Sin Ɵ=a/h≈ 0
tan Ɵ=a/b≈ 0

besides, it should be noticed that h and b are almost the same height with h being only slightly
longer and hence
cos Ɵ=b/h≈ 1
b≈h and hence a/h≈a/b and thus sin Ɵ≈tan Ɵ
ii. When the C=9⁰;
10
sin 81 = AB
sin 9
AB= 10 sin 9
sin 81 =4.173 units
10
sin 81 = AC
sin 90
AC= 10 sin 9 0
sin 81 =10.12 units
Question 2: Applications of Trigonometric Functions
(a) Scalene triangle. Neither of the sides nor the angles is equal
(b) a2 =b2+c2-2bc cos A
=202+302-2*30*20 cos 25
a=√212.4=14.57 units
(c) b
sin B = a
sin A

30
sin B = 14.57
sin 25
sin B= 30 sin 25
14.57 =0.871
B=60.57⁰
(d) c
sin C = a
sin A
30
sin C = 14.57
sin 25
sin C= 20 sin25
14.57 =0.581
C=35.52⁰
(e) Area of the triangle
A= √s (s−a)(s−b)(s−c )
S=p/2= (20+30+14.57)/2=32.3
A= √32.3 (32.3−30)(32.3−20)(32.3−14.57)
√32.3 ×2.3 ×12.3 ×17.73=127.28 sq. units
Question 3: Trigonometric Functions of Real Numbers
(a)