Thread: How to find the value of sin45 degrees?

As far as I know sine has values between 1 and -1 therefore I don't know how to calculate this kind of questions with calculator! Could you help me please...

Wrong question! Sorry

For the record 45 degrees is on the unit circle

My personal favorite is to do it by the unit circle, File:Unit circle.svg - Wikipedia, the free encyclopedia

In this particular case, the angle t = 45 degrees, using the notation in the picture.

Now, we are going to use two basic facts about triangles, the Pythagorean theorem as well as the basic definition of the sine-function. First off, the sum of the angles in a triangle is 180. Meaning that if you know one angle is 90 and one is 45, you know that the third is 180-90-45 = 45 degrees

Having two equal angles, we know that the two sides not drawn in the picture are the same length. And since we're working in a unit circle, we know that the side drawn, the hypotenuse of the triangle, is 1. Thus, if we call the sides S we know by the Pythagorean theorem that
S^2 + S^2 = 1
or
S = 1/sqrt(2) [sqrt(2) means the square root of two!]

Now, all we need to do is take the basic definition of the sine-function in a right triangle, that is
sin(t) = opposite/hypotenuse

In our case we have sin(45) = (1/sqrt(2))/1 = 1/sqrt(2)

Hope that helps a little and wasn't just all confusing. My recommendation would be to step back and review the stuff I mentioned in the second paragraph; if you have that down this will be a piece of cake.

45 degrees is exactly half of 90 degrees. Since the two non-right angles in a right triangle add to 90 degrees, that means that if one angle is 45 degrees so is the other- a 45, 45, 90 degree triangle is isosceles. If one leg has length, say, 1, so does the other. By the Pythagorean theorem, the length of the hypotenuse, c , is given by so . Now, sine is "opposite side/hypotenuse" so and, "rationalizing the denominator, that is .