SOLUTION: Find the value of cot(cos^-1 2/3)

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Question 616286: Find the value of cot(cos^-1 2/3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. Draw a right triangle
  2. Pick one of the acute angles. Let's call it angle A.
  3. Label the side adjacent to angle A as 2 and the hypotenuse as 3. Since cos is adjacent over hypotenuse, we have just made cos(A) = 2/3
  4. Since cot is adjacent over opposite, we need the opposite side. Use the Pythagorean Theorem to find the side opposite to angle A.
  5. cot%28cos%5E%28-1%29%282%2F3%29%29 will be adjacent over opposite, 2 over the answer from the previous step.
  6. At this point you may have an acceptable answer. But it will have a square root in the denominator. You may want/need to rationalize the denominator. Just multiply the numerator and denominator by the square root in the denominator and simplify.