How do you evaluate #sin45°#?

1 Answer
Zor Shekhtman
Jul 31, 2015

#sin(45^o)=sqrt(2)/2~~0.7071...#

Explanation:

An angle of #45^o# is an angle in the right triangle with equal catheti because another acute angel must be #45^o# as well..
So, if a cathetus equals to #a#, another is #a# as well and hypotenuse, according to Pythagorean Theorem, equals to #sqrt(a^2+a^2)=a*sqrt(2)#.

Therefore, #sin(45^o)#, as the ratio of a cathetus opposite to this angle to a hypotenuse, equals to #a/(a*sqrt(2))=1/sqrt(2)=sqrt(2)/2#.

As for evaluation of #sin(45^o)#, we just have to calculate the value of #sqrt(2)/2#, which is approximately #0.7071...#

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