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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 $\theta$ .


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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. $\text{cosec} ^2{\theta}-1$
in Mathematics by Platinum (98.5k points) | 2.4k views

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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 Gold Status (26.7k points)
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