Final answer:
The sine of 135 degrees is \(\frac{\sqrt{2}}{2}\), the cosine is \(-\frac{\sqrt{2}}{2}\), and the tangent is -1, based on the reference angle of 45 degrees and the knowledge that in the second quadrant, sine is positive while cosine and tangent are negative.
Step-by-step explanation:
To find the sine, cosine, and tangent of an angle, we use the definitions of these trigonometric functions in terms of a right triangle's sides. For an angle of 135 degrees, which lies in the second quadrant, where sine is positive and cosine and tangent are negative, we can use reference angles to calculate the values.
The reference angle for 135 degrees is 45 degrees, since it's 180 - 135. The sine and cosine of 45 degrees are equal, at \(\frac{\sqrt{2}}{2}\), and the tangent is 1. However, since 135 degrees is in the second quadrant, the cosine and tangent will be negative, while the sine will remain positive.
Therefore, the sine of 135 degrees is \(\frac{\sqrt{2}}{2}\), the cosine of 135 degrees is \(-\frac{\sqrt{2}}{2}\), and the tangent of 135 degrees is -1. These values can be calculated using a calculator or by recalling common trigonometric values for standard angles.