Trigonometry Question

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Consider the arc of length s on the unit circle that begins at the point (1, 0) and ends at the point (−0.4898, −0.7864). Find csc s, sec s, cot s.

Oct 8th, 2015

Thank you for the opportunity to help you with your question!

In general the coordinates of a point P  on a unit circle are given by 

( cos θ. sin θ) where  θ is the angle at the center from (1, 0) to the point P measured in radians (anticlockwise)

Since the point P  is (−0.4898, −0.7864)

we conclude that cos θ. = −0.4898  and  sin θ = −0.7864

From these, we can find the other ratios:

csc  θ = 1/sin θ 

              = 1/−0.7864

           = -1.2716

sec  θ = 1/cos θ  

            = 1/−0.4898 


and cot θ = cos θ/sin θ  

               =   −0.4898/ −0.7864 

                   = 0.6228

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 8th, 2015

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