If cosec θ = √10, the find the values of all T-ratios of θ.

Question

Harshit Singh · Answer

Dear Student Given function: cosec&theta; = &radic;10 Draw a right ∆ABC,&ang;C = 90 degrees and&ang;A = &theta; We know that, cosec&theta; = hypotenuse/perpendicular = (k&radic;10)/k where k is a positive integer By Pythagoras Theorem: AC^2 = AB^2 + BC^2 = 10k^2 + k^2 = 9k^2 AC = 3k Find other T-rations using their definitions: Sin𝜃= BC/AB = 1/&radic;10 cos𝜃= AC/AB = (3k)/(k&radic;10) = 3/&radic;10 tan &theta; = BC/AC = sin&theta; /cos&theta; = 1/3 sec&theta; = AB/AC = 1/cos&theta; = &radic;10/3 cot&theta; = AC/BC = 1/tan&theta; = 3 Thanks

Ram Kushwah · Answer

From the fig we know that cosecθ =Hypotenuse/Height =AC/AB=√10/1=√10 Using pythagoras theorem in the Δ ABC BC²=AC²-AB² =(√10)²-1²=10-1=9 so BC= √9 = 3 Thus the other T-ratios can be written as : sin θ =AB/AC = 1/ √ 10 cos θ=BC/AC= 3/ √ 10 tanθ=AB/BC= 1/3 cotθ=BC/AB= 3/1= 3 secθ=AC/BC= √ 10/3 Thanks

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If cosec θ = √10, the find the values of all T-ratios of θ.

If cosec θ = √10, the find the values of all T-ratios of θ.

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