Question

How do you evaluate `sin45°`?

Answer 1

`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...`