Inverse Trigonometric Functions Question?

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Inverse Trigonometric Functions Question?

Use a sketch to find the exact value of each expression.

cos [tan-1 (-2/3)]

I need help with this problem. Correct answer gets 10 points.

2007-10-24 10:13:23 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

Since tan-1 (-2/3)] is in the fourth quadrant, we have
cos [tan-1 (-2/3)] = 3/sqrt(13)
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Ideas: 2, 3 and sqrt(13) form a right triangle.

2007-10-24 10:20:46 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋

lot O(0,0), A(-3,0), and B(-3,2 Then the angle AOB has a tan = AB/OA = -2/3. So OB = sqrt(3^2+2^2) = sqrt(13)
So cos angle AOB = -3/sqrt(13) = -3sqrt(13)/13

2007-10-24 17:27:34 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋