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Given sec θ = 13/12 . Calculate all other trigonometric ratios and please tell it asap

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one month ago Anand Kumar Pandey
1372 Points
```							Dear StudentWe know thatsec function is the reciprocal of the cos functionwhich is equal to the ratio of the length of the hypotenuse side to the adjacent sideLet us assume a right angled triangle ABC, right angled at Bsec θ =13/12 = Hypotenuse/Adjacent side = AC/ABLet AC be 13k and AB will be 12kWhere, k is a positive real number.According to the Pythagoras theorem,the squares of the hypotenuse side is equal to the sum of the squares of the other two sides of a right angle triangleand we get,AC^2=AB^2+ BC^2Substitute the value of AB and AC (13k)^2= (12k)^2+ BC^2169k^2= 144k^2+ BC^2169k^2= 144k^2+ BC^2BC^2 =169k^2- 144k^2BC^2= 25k^2Therefore, BC = 5kNow, substitute the corresponding values in all other trigonometric ratios So,Sin θ =Opposite Side/Hypotenuse = BC/AC = 5/13Cos θ =Adjacent Side/Hypotenuse = AB/AC = 12/13tan θ =Opposite Side/Adjacent Side = BC/AB = 5/12Cosec θ =Hypotenuse/Opposite Side = AC/BC = 13/5cotθ =Adjacent Side/Opposite Side = AB/BC = 12/5these are required valuesThanks
```
one month ago
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