What is sin pi over 4?

Answer 1

What does sin(pi/4) = ?

Let's consider a special right triangle: the 45-45-90 triangle.

In any 45-45-90 triangle, since the two 45 degree angles are congruent, the sides opposite to those angles are both congruent.

Now, considering the unit circle, the radius of the circle must be one.

So, if you put in a 45-45-90 triangle in a unit circle, this allows you to find the value of sin pi/4 because pi/4 radians = 45 degrees.

Because the circle has radius 1, the hypotenuse of the triangle must also be one. Since the other two sides must be equal, you can solve for them using the Pythagorean theorem.

a2 + b2 = c2

a2 + a2 = 12

2a2 = 1

a2 = 1/2

a = √(1/2)

a = 1/√(2) * (√(2)/√(2))

a = √(2) / 2

Since sin is defined as opp/hyp, sin 45 degrees (pi/4 radians) = (√(2)/2)/1 = √(2)/2

I hope this helped explain my answer. If there's anything that's still confusing, just tell me. (Sorry I didn't do it the first time).

Answer 2

Sin(pi/4) = sqrt(2)/2 = 0.707106.....