If cot (theta) = (frac{x}{y}), find cosec(theta)
-
A.
(frac{1}{y})(x2 + y2) -
B.
(frac{x}{y}) -
C.
(frac{1}{y})(sqrt{x^2 + y^2}) -
D.
(frac{x – y}{y})
Correct Answer: Option C
Explanation
(cot theta = frac{x}{y})
(implies tan theta = frac{y}{x})
(opp = y; adj = x)
Using Pythagoras theorem, (Hyp^{2} = Opp^{2} + Adj^{2})
(Hyp^{2} = y^{2} + x^{2})
(Hyp = sqrt{y^{2} + x^{2}})
(sin theta = frac{y}{sqrt{y^{2} + x^{2}}})
(therefore csc theta = frac{sqrt{y^{2} + x^{2}}}{y})
= (frac{1}{y}(sqrt{y^{2} + x^{2}}))