Question

If sin theta=1/root2 find the value of other trigonometrical ratios for theta

Answer 1

sin theta=1/√2
sin^2Q=1/2
cos^2Q=1-sin^2Q
cos^2Q=1-1/2
=1/2
cosQ=1/√2
tanQ=sinQ/cosQ
tanQ=1
cosecQ=1/sinQ
cosecQ=√2
secQ=1/cosQ
secQ=√2
cotQ=1/tanQ
cotQ=1

Answer 2

Cosθ  = ±1/√2 , Tanθ   =  ±1 , Cotθ = ±1 , Cosecθ  = √2  , Secθ  = ±√2  if Sinθ  = 1/√2

Step-by-step explanation:

Sinθ  = 1/√2

Sin²θ = 1/2

Cos²θ  = 1 - Sin²θ

=> Cos²θ  = 1 - 1/2

=> Cos²θ  =  1/2

=> Cosθ  = ±1/√2

Tanθ  = Sinθ /Cosθ

=> Tanθ   =  (1/√2)/( ±1/√2)

=>  Tanθ   =  ±1

Cotθ = 1/Tanθ  = ±1

Cosecθ  = 1/Sinθ  = 1/(1/√2) =   √2

Secθ  = 1/Cosθ  = 1/( ±1/√2) =   ±√2

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