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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