find exact value of sin 495 degrees without a calculator?
Another way to find the answer without a calculator is to first get it to an angle between 0 and 360 degrees by subtracting 360 until you are in the range. That’s because of “periodicity”. Like the loading station on a Ferris wheel or a merry-go-round, once you go all the way around the circle (360), you are back at the same place.
495 - 360 = 135, OK, now a 135 degree angle is the same as a 45 degree angle in the second quadrant. Algebra students should memorize the sides of 45/45/90 and 30/60/90 triangles. In this case, the opposite side (y-value) is 1, the adjacent side (x-value) is -1, because we are in the second quadrant, and the hypotenuse, using Pythagorean theorem, is sqr rt 2. So, the sin 495 degrees is 1/sqr rt 2 or, rationalizing the denominator, is sqr rt 2/ 2.