SOLUTION: find the exact value of cotangent theta if theta is in standard position and (-7,2) is on the terminal side of theta

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Question 618317: find the exact value of cotangent theta if theta is in standard position and (-7,2) is on the terminal side of theta
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
To understand this better, it will help to have a diagram:
Plot the point (-7, 2) on a coordinate system.
Draw a line segment from the origin to the point.
Draw a line segment from the point down to the x axis.
These two segments plus part of the x axis form a right triangle.
Label the angle in the triangle whose vertex is at the origin as angle A.
Label the horizontal side (on the x axis) as -7. This is the adjacent side to angle A.
Label the vertical side as 2. This is the opposite side to angle A.

is the angle measured from the positive part of the x axis to the hypotenuse of the triangle. It is not in the triangle we just drew. But angle A is the reference angle for . So we can use the reference angle's opposite and adjacent sides to find cotangent.

Since cotangent is adjacent over opposite: