9.3.1 Trigonometry II, SPM Paper 1 (Short Questions)


Question 1:


In the diagram above, find the value of tan θ.

Solution:

In A B C , using Pythagoras’ Theorem, A C = 1 2 + 1 2 = 2 c m tan θ = C D A C tan θ = 1 2


Question 2:



In the diagram above, ABCE is a rectangle and point D lies on the straight line EC. Given that DC = 5 cm and AE = 4cm, find the value of cosθ.

Solution:
AD=DC=5cm In  AED, using Pythagoras’ Theorem, ED= 5 2 4 2 =3cm cosθ=cosADE Since  90 <θ< 180 (in quadrant II), cosθ is negative cosθ= ED AD cosθ= 3 5



Question 3:



In the diagram above, PMR is a straight line, M is the midpoint of line PR. Given that QR = 12cm and sin y°= 0.6, find the value of tan x°.

Solution:
In triangle QMR sin y =0.6 sin y = QR QM = 6 10 Given QR=12cm, QM=10×2=20cm In  QMR, using Pythagoras’ Theorem, MR= 20 2 12 2 =16cm PR=16×2=32cm Hence tan x = QR PR = 12 32 = 3 8

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