document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #388847 by jsmallt9(3758) $\"\"$ $\"About$

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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.

\n" ); document.write( " $\"theta\"$ 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 $\"theta\"$ . So we can use the reference angle's opposite and adjacent sides to find cotangent.

\n" ); document.write( "Since cotangent is adjacent over opposite:
\n" ); document.write( " $\"cot%28theta%29+=+%28-7%29%2F2\"$ \n" ); document.write( "

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