Solve for the following trigonometric ratios using quadrants.
a) tan135
To solve for tan(135), we need to find the tangent of an angle of 135 degrees.
In the first quadrant, the tangent is positive.
In the second quadrant, the tangent is negative.
In the third quadrant, the tangent is positive.
In the fourth quadrant, the tangent is negative.
135 degrees lies in the second quadrant, so the tangent of 135 degrees is negative.
Since tan(135) is negative, we can write:
tan(135) = -tan(45)
We know that tan(45) = 1, so:
tan(135) = -1