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Question: Find the value of tan θ and sec θ for an angle θ in the standard position if the point Q(- 12, 5) is on its terminal side.


A ) - 512, - 1213
B ) 512, 1312
C ) - 125, - 1312
D ) - 512, - 1312

Steps to derive

1 The co-ordinates of Q are (- 12, 5), so Q lies in quadrant II.


2 r = x2+y2 = (-12)2+52
 [Replace x = - 12 and y = 5.]

3 = 144 + 25 = 169 = 13
 [Simplify.]

4 tan θ = yx = 5- 12 = - 512
 [Replace x = - 12 and y = 5.]

5 sec θ = rx = 13- 12 = - 1312
 [Replace x = - 12 and r = 13.]



Hence the right answer is Option D

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