Question

If sin θ =11/61 find the values of the other trigonometric ratios.

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

We have, sin θ = 11/15 ………. (1)

By definition,

sin θ = Perpendicular/ Hypotenuse …. (2)

On Comparing eq. (1) and (2), we get;

Perpendicular = 11 and Hypotenuse= 15

Now, using Pythagoras theorem in Δ ABC

AC2 = AB2 + BC2

Putting the value of perpendicular (BC) and hypotenuse (AC) to get the base (AB), we have

152 = AB2 +112

AB2 = 152 – 112

AB2 = 225 – 121

AB2 = 104

AB = √104

AB= √ (2×2×2×13)

AB= 2√(2×13)

AB= 2√26

Hence, Base = 2√26

By definition,

cos θ = Base/Hypotenuse

∴ cosθ = 2√26/ 15

And, cosec θ = 1/sin θ

∴ cosec θ = 15/11

And, secθ = Hypotenuse/Base

∴ secθ =15/ 2√26

And, tan θ = Perpendicular/Base

∴ tanθ =11/ 2√26

And, cot θ = Base/Perpendicular

∴ cotθ =2√26/ 11