Cot 495 degrees... a) -tan 135 degrees
b) -cot 135 degrees
c) cot 135 degrees
d) -cot 315 degrees
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cot 135 degrees
495 - 360 = 135
cot 495° = cot 135°
To find the value of cot 495 degrees, we need to use the relationship that cotangent is the reciprocal of tangent. Therefore, we can find the value of cot 495 degrees by finding the value of tan 495 degrees and then taking its reciprocal.
To find the value of tan 495 degrees, we can use the periodicity property of the tangent function, which states that tan (angle + 180 degrees) = tan (angle). This means that we can subtract 360 degrees from 495 degrees to find an equivalent angle within one revolution.
495 degrees - 360 degrees = 135 degrees
Now, we need to find the value of tan 135 degrees. To do this, we can use the unit circle or a calculator to evaluate the tangent of 135 degrees.
Using the unit circle, we know that at 135 degrees, the coordinates of the point on the unit circle are (-√2/2, -√2/2).
Therefore, the value of tan 135 degrees is -1.
Now, we take the reciprocal of -1 to find the value of cot 495 degrees.
The reciprocal of -1 is -1, so the correct answer is:
b) -cot 135 degrees