Math CentralQuandaries & Queries


Question from Stephanie, a student:

Why isn't there really a solution for the equation: cosX= -1.25?

Hi Stephanie.

Maybe you remember the mnemonic SOH CAH TOA, this reminds us that the cosine of an angle in a right-angled triangle is the adjacent side over the hypotenuse.

But we also know that the hypotenuse is always the longest side in a right angled triangle.

This means that the adjacent side (the numerator) can never be more than the hypotenuse (the denominator), so the magnitude (ignoring the plus or minus sign) of the ratio adjacent-over-hypotenuse is never more than 1.

Therefore -1.25 is not possible as the cosine of any angle.

Stephen La Rocque.

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