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

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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) About Me  (Show Source):
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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) About Me  (Show Source):
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because decimal 0.7071067812+ is approximate value and missing more decimal places,the EXACT value of cos%2845%29° is 1%2Fsqrt%282%29

Answer by ikleyn(52803) About Me  (Show Source):
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.

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



Answer by MathTherapy(10552) About Me  (Show Source):
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Explain why 0.7071067812 is not the EXACT value of cos 45°
0.7071067812 is an APPROXIMATE value for cos+%2845%5Eo%29, while sqrt%282%29%2F2 is its EXACT value. 

Can't get more EXACT than that!!