How do you find cot(225degrees) using the unit circle?
Draw the unit circle, and draw the line making an angle of 225° with the +x axis.
That line intersects the circle at (-1,-1)
cos225° = x/y = -1/1 = 1
Thank you :)
To find the value of cot(225 degrees) using the unit circle, follow these steps:
1. Draw a unit circle by drawing a circle with a radius of 1 unit.
2. Label the points on the unit circle in increments of 30 degrees. For example, label the points at 0 degrees, 30 degrees, 60 degrees, and so on, up to 360 degrees.
3. The point on the unit circle where the angle is 225 degrees is in the third quadrant, between 180 degrees and 270 degrees.
4. Notice that in the third quadrant, the x-coordinate is negative, while the y-coordinate is also negative.
5. Since cotangent is the reciprocal of tangent, we can find the value of tangent (tan) at 225 degrees and then take its reciprocal to find the cotangent (cot).
6. To find the tangent (tan) of 225 degrees, we need to find the ratio of the y-coordinate to the x-coordinate at that point on the unit circle.
7. In the third quadrant, the y-coordinate is negative, and the x-coordinate is negative as well. So, we have:
- y-coordinate = -√2/2
- x-coordinate = -√2/2
8. Therefore, the tangent (tan) of 225 degrees can be calculated as:
tan(225 degrees) = (y-coordinate / x-coordinate) = (-√2/2) / (-√2/2) = 1
9. Finally, the cotangent (cot) of 225 degrees is the reciprocal of the tangent (tan):
cot(225 degrees) = 1/1 = 1
So, cot(225 degrees) = 1.