They have to be equal with opposite sign so they can cancel each other out.
When x = 45 degrees, sin(x) and cos(x) are the same = .707106781
That's because they're in the first quadrant and sin(x) and cos(x) are both positive because:
opposite = length of the line is always positive.
adjacent is distance on the x-axis to the right of the y-axis and is positive.
opposite is distance on the y-axis up from the x-axis and is positive.
Go to the second quadrant and form 45 degrees up from 180 degrees.
hypotenuse is positive.
adjacent is negative (left of y-axis)
opposite is positive (up from x-axis)
the values are the same but now the sin(x) is positive and cos(x) is negative.
180 - 45 = 135 so we are talking about sin(135) and cos(135).
