When using the half-angle formulas for trigonometric functions of α2, I determine the sign based on the quadrant in which α lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

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Cristiano Sears · Accepted Answer

For example: The trigonometric function is given as, cos⁡(112.5∘) cos⁡(112.5∘)=cos⁡(225∘2) Here, α=225∘ Apply the half angle formula for the given trigonometric function, cos⁡(112.5∘) in which the angle 112.5∘ lies in the quadrant (II) where sine and cosecant is positive. We have to determine the value of cos⁡(112.5∘) which is negative in second quadrant. Therefore in half angle formula , negative sign has to be put. cos⁡(α2)=−1+cos⁡α2 The value of cos⁡(112.5∘)=cos⁡(225∘2)is, cos⁡(225∘2)=−1+cos⁡225∘2 =1+(−22)2 =−(2−22)

Jeffrey Jordon · Accepted Answer

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When using the half-angle formulas for trigonometric functions of alpha/2, I determine the sign based on the quadrant in which alpha lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

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