How do you evaluate sin(π/4)?

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How do you evaluate sin(π/4)?

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Answer 1 · 2016-02-11T23:15:27

$sqrt(2)/2$

Explanation:

In the trigonometric circle $pi/4$ is the bisectrix between 0 and $pi/2$ , where x=y.
By the Pythogoras theorem we know that $x^2+y^2=1$ .

If you don't know the trigonometric circle, you can see that if one of the small angles of a rectangle triangle is $pi/4$ , the other will be also $pi/4$ , which implies the catets are equal.

So if x=y, you will have

$x^2+y^2=1$

$2y^2=1$

$y^2=1/2$

$y=sqrt(1/2)=sqrt(2)/2$

To get the sin of $pi/4$ you divide the opposite catet ( $sqrt(2)/2$ )
by the hypothenuse( 1).

You'll get $sqrt(2)/2$

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How do you evaluate sin(π/4)?

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