What is the sin of 495 degrees?
495 - 360 = 135
sin 135 = sin (180 -135) = sin 45 = 1/sqrt2 = sqrt 2/2 = .707
To determine the sine of an angle, we can use trigonometric functions. The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.
However, it's important to note that angles greater than 360 degrees (or 2π radians) are not within the range of the unit circle. So, when dealing with angles larger than 360 degrees, we need to convert them to an equivalent angle within the range.
To convert 495 degrees to an equivalent angle within the range, we can subtract multiples of 360 degrees until we obtain an angle less than 360 degrees. In this case:
495 degrees - 360 degrees = 135 degrees
Thus, the sine of 495 degrees is equal to the sine of 135 degrees.
Now, the sine function for 135 degrees can be determined:
sin(135 degrees) = (√2)/2
Therefore, the sin of 495 degrees is (√2)/2.
To find the sine of an angle, we need to first convert the angle from degrees to radians. The formula to convert from degrees to radians is:
radians = degrees * π / 180
Using this formula, we can convert 495 degrees to radians:
radians = 495 * π / 180
Next, we can calculate the sine of the angle using a scientific calculator or the sine function on a programming language. The sine function returns the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
sin(495 degrees) = sin(radians)
The exact value of the sine of 495 degrees depends on the level of precision required. As an approximate value, the sine of 495 degrees is about -0.8910065242.