Trigonometry Short Questions (Question 1 – 3)


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:
A D = D C = 5 c m In A E D , using Pythagoras’ Theorem, E D = 5 2 4 2 = 3 c m cos θ = cos A D E Since 90 < θ < 180 ( in quadrant II), cos θ is negative cos θ = E D A D cos θ = 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 Q M R , sin y = 0.6 sin y = Q R Q M = 6 10 Given Q R = 12 c m , Q M = 10 × 2 = 20 c m In Q M R , using Pythagoras’ Theorem, M R = 20 2 12 2 = 16 c m P R = 16 × 2 = 32 c m Hence tan x = Q R P R = 12 32 = 3 8

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