Question

If cosecθ = √10, then find the values of other t–ratios of angle θ.

Answer 1

Step-by-step explanation:

We know that,

cosecθ = Hypotenuse / Opposite side to theta

cosecθ = √10 / 1

Hypotenuse = √10

Opposite side = 1

By Pythagoras theorem,

( Hypotenuse )² = (Adjacent side) ²+ (Opposite side) ²

Adjacent side = √[ ( √10)² - 1² ] = √9 = 3

Now, Trigonometry ratios :

cosθ = Adjacent side to theta / Hypotenuse = 3/√10

sinθ = Opposite side of theta / Hypotenuse = 1/√10

tanθ = sinθ/cosθ = 1/3

cotθ = 1/tanθ = 1/( 1/3) = 3

secθ = 1/cosθ = 1/(3/√10) = √10/3

∴ The trigonometric ratios , cosθ = 3/√10 , sinθ = 1/√10 , tanθ = 1/3 , cotθ = 3 , secθ = √10/3

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