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In the diagram below, P(12;-5) is a point in a Cartesian plane with origin O(0 ; 0). The reflex angle that is formed by OP with the positive x-axis is $\theta$ .

Determine, without using a calculator, the value of each of the following:

1. The length of OP
2. $5\cot{\theta}-13\cos{\theta}$
3. $\text{cosec} ^2{\theta}-1$
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1. OP^2 =  12^2 + (-5)^2
OP =13 units

2. 5cotx -13cosx
=5(12/-5) -  13(12/13)

= -24

3. cosec - 1
= (13/-5)^2 - 1
= 144/25
by Silver Status (31.3k points)

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