SOLUTION: Explain why 0.7071067812 is not the EXACT value of cos 45°

Question 1159350: Explain why 0.7071067812 is not the EXACT value of cos 45°
Found 4 solutions by Boreal, MathLover1, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
In a 45-45-90 triangle, the sides are 1/1/sqrt(2)
the cosine is 1/sqrt(2) or sqrt (2)/2
That is the exact answer. Anything else is rounding.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

because decimal is approximate value and missing more decimal places,the EXACT value of ° is
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Because the exact value of cos(45°) is an IRRATIONAL number, while the number 0.7071067812 is RATIONAL.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Explain why 0.7071067812 is not the EXACT value of cos 45°

0.7071067812 is an APPROXIMATE value for , while is its EXACT value.
Can't get more EXACT than that!!
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