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

Harshit Singh
9 months ago
Dear Student

Given function: cosecθ = √10
Draw a right ∆ABC,∠C = 90 degrees and∠A = θ

We know that, cosecθ = hypotenuse/perpendicular
= (k√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/√10

cos𝜃= AC/AB = (3k)/(k√10) = 3/√10

tan θ = BC/AC = sinθ /cosθ = 1/3

secθ = AB/AC = 1/cosθ = √10/3

cotθ = AC/BC = 1/tanθ = 3

Thanks
Ram Kushwah
110 Points
5 months ago

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