Given sec calculate all other trigonometric ratios

Consider a right-angle triangle ΔABC, right-angled at point B


sec =


=


If AC is 13k, AB will be 12k, where k is a positive integer.


Applying Pythagoras theorem in ΔABC, we obtain


(AC)2 = (AB)2 + (BC)2


(13k)2 = (12k)2 + (BC)2


169k2 = 144k2 + BC2


25k2 = BC2


BC = 5k


Sin =


= =


Cos θ =


= =


Tan θ =


= =


Cot θ =


= =


Cosec θ =


= =


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