Question 15 (4 marks):
It is given that cos α = t where t is a constant and 0o ≤ α ≤ 90o.
Express in terms of t
(a) sin (180o + α),
(b) sec 2α.
Solution:
(a)
sin(180o+α)=sin180cosα+cos180sinα=0−sinα=−sinα=−√1−t2
(b)
sec2α=1cos2α =12cos2α−1 =12t2−1
It is given that cos α = t where t is a constant and 0o ≤ α ≤ 90o.
Express in terms of t
(a) sin (180o + α),
(b) sec 2α.
Solution:
(a)
sin(180o+α)=sin180cosα+cos180sinα=0−sinα=−sinα=−√1−t2
(b)
sec2α=1cos2α =12cos2α−1 =12t2−1
Question 16 (3 marks):
Diagram 7 shows two sectors AOD and BOC of two concentric circles with centre O.
Diagram 7
The angle subtended at the centre O by the major arc AD is 7α radians and the perimeter of the whole diagram is 50 cm.
Given OB = r cm, OA = 2OB and ∠BOC = 2α, express r in terms of α.
Solution:
Length of major arc AOD=2r×7α=14rαLength of minor arc BOC=r×2α=2rαPerimeter of the whole diagram=50 cm14rα+2rα+r+r=5016rα+2r=508rα+r=25r(8α+1)=25r=258α+1
Diagram 7 shows two sectors AOD and BOC of two concentric circles with centre O.
Diagram 7
The angle subtended at the centre O by the major arc AD is 7α radians and the perimeter of the whole diagram is 50 cm.
Given OB = r cm, OA = 2OB and ∠BOC = 2α, express r in terms of α.
Solution:
Length of major arc AOD=2r×7α=14rαLength of minor arc BOC=r×2α=2rαPerimeter of the whole diagram=50 cm14rα+2rα+r+r=5016rα+2r=508rα+r=25r(8α+1)=25r=258α+1