Find an algebraic expression equivalent to tan ( arc cos X ) Evaluate: arc cos ( cos pi/3) arc cos ( cos -pi/7)
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Originally Posted by Godfather Find an algebraic expression equivalent to tan ( arc cos X ) Evaluate: arc cos ( cos pi/3) arc cos ( cos -pi/7) Draw a reference triangle using the defintion of the cosine function... 1 will be the hypotenuse and x will be the adjacent side.... solve for the opposite side using the pythagorean theorem. Using the definition of tangent gives
Last edited by TheEmptySet; Feb 24th 2008 at 10:00 AM. Reason: I hit the wrong button
For the second part.... We need to know the domain of the arc cosine function.... The domain is 0 to Pi. also note that the cosine function is even ie This gives us so and since the angle is now in the domain of the arc sine function.
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