Question 5
Given secθ = 1312, calculate all other trigonometric ratios.
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Solution
Let ΔPOM be a right-angled triangle, right-angled at M.
We know that sec θ = OPOM = 1312
Let OP be 13k and OM will be 12k where k is a positive real number.
By Pythagoras theorem; we get, OP2=OM2+MP2 (13k)2=(12k)2+MP2 169k2−144k2=MP2 MP2=25k2
MP = 5k
Now, sinθ = MPOP = 5k13k = 513 cosθ = OMOP = 12k13k = 1213 tanθ = MPOM = 5k12k = 512 cotθ = OMMP = 12k5k = 125 cosecθ = OPMP = 13k5k = 135