Sanarah
Answered

Find the exact value of the trig function below.


cos\(\frac{ \alpha }{2}\) if cos\(\alpha\) = \(\frac{-31}{49}\)


(assume cos\(\frac{ \alpha }{2}\) is negative)

Verified Answer :

AbhiGhost

Since value is negative, therefore answer should be 3/7. Hope this helps.

View image AbhiGhost

cos (α/2)=⁺₋√[(1+cos α)/2]

Assume cos (α/2) is negative; therefore
cos (α/2)=-√[(1+cos α)/2]
cos (α/2)=-√[(1-(31/49))/2]
cos (α/2)=-√[(18/49)/2]
cos (α/2)=-√(18/98)

Answer: cos (α/2)=-√(18/98)                    (≈-0.42857...)

We can check it out our answer:
α=cos⁻¹ (-31/49)≈230.75
α/2 =cos⁻¹(-√(18/98)≈115.37
α/2=230.75 /2 =115.37

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