What is the exact value of csc θ?
I'm having some issues with this problem...I'm not sure how the coordinates play into solving the problem. Could anyone please point me in the right direction?
What is the exact value of the csc θ if (5,2) is on the terminal side of θ in standard position?
(1) -5/2
(2) 5√29/29
(3) -√29/2
(4) √29/2
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Recognizing that the cosecant of an angle is, by definition, the hypotenuse of a right triangle divided by the side opposite the angle, or the reciprocal of the sine of the angle.
If the terminal side of the angle in standard position contains the point (x,y) = (5,2) then the side opposite the angle is the y value, 2, and the hypotenuse is √(5²+2²) = √29
The cosecant is hypotenuse divided by side opposite or csc(Θ) = √29/2
Hypotenuse/Opposite = sqrt(29)/2