Question

If cosec0=√10 find the values of all T ratios of 0​

Answer 1

We have, cosecθ = (k√10)/k = 1/sinθ (For some value of k)

→ sinθ = k/(k√10) = perpendicular/hypotenuse

By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2

∴AB2 = BC2 + AC2

(√10k)2 = (k)2 + AC2

AC2 = 10k2 - k2

AC2 = 9k2 = (3k)2

→ AC = 3k

Hence, the trignometeric ratios for the given θ are:

sinθ = 1/√10

cosθ = AC/AB = (3k)/(k√10) = 3/√10

tanθ = BC/AC = sinθ /cosθ = 1/3

cotθ = AC/BC = 1/tanθ = 3

cosecθ = √10

secθ = AB/AC = 1/cosθ = √10/3

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