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your interval is from 0 radians to 2 * pi radians which is equivalent to:
\n" ); document.write( "from 0 degrees to 360 degrees.
\n" ); document.write( "first you want to solve for cotangent theta = .4291
\n" ); document.write( "since cotangent theta is equal to 1 / tangent theta, your equation becomes:
\n" ); document.write( "1 / tangent theta = .4291
\n" ); document.write( "multiply both sides of this equation by cotangent theta and divide both sides of this equation by .4291 to get:
\n" ); document.write( "1 / .4291 = tangent theta.
\n" ); document.write( "simplify to get:
\n" ); document.write( "tangent theta = 2.331002331
\n" ); document.write( "to find theta, you take the arc tangent of 2.331002331 to get:
\n" ); document.write( "theta = 66.78066768 degrees.
\n" ); document.write( "that's the value of theta if theta is in the first quadrant.
\n" ); document.write( "in the first quadrant, tangent is positive and cosine is positive, so your answer can't be in the first quadrant because cosine theta has to be less than 0 which means cosine theta must be negative.
\n" ); document.write( "tangent theta is positive in the first quadrant and in the third quadrant.
\n" ); document.write( "cosine theta is negative in the second quadrant and in the third quadrant.
\n" ); document.write( "since the third quadrant allows tangent to be positive and cosine to be negative, your answer must be in the third quadrant.
\n" ); document.write( "the equivalent angle in the third quadrant that has the same tangent as an angle in the first quadrant would be equal to 180 + 66.78066768 degrees which makes the angle equal to 246.7806677 degrees.
\n" ); document.write( "the equivalent angle in radians is equal to 246.7806677 * pi / 180 which is equal to 1.371003709 * pi radians which is equivalent to 4.307135181 radians.
\n" ); document.write( "-----
\n" ); document.write( "if you had not converted to degrees, but worked in radians from the beginning, you would have done the following:
\n" ); document.write( "your interval is from 0 radians to 2 * pi radians.
\n" ); document.write( "first you want to solve for cotangent theta = .4291
\n" ); document.write( "since cotangent theta is equal to 1 / tangent theta, your equation becomes:
\n" ); document.write( "1 / tangent theta = .4291
\n" ); document.write( "multiply both sides of this equation by cotangent theta and divide both sides of this equation by .4291 to get:
\n" ); document.write( "1 / .4291 = tangent theta.
\n" ); document.write( "simplify to get:
\n" ); document.write( "tangent theta = 2.331002331
\n" ); document.write( "to find theta, you take the arc tangent of 2.331002331 to get:
\n" ); document.write( "theta = 1.165542528 radians
\n" ); document.write( "that's the value of theta if theta is in the first quadrant.
\n" ); document.write( "in the first quadrant, tangent is positive and cosine is positive, so your answer can't be in the first quadrant because cosine theta has to be less than 0 which means cosine theta must be negative.
\n" ); document.write( "tangent theta is positive in the first quadrant and in the third quadrant.
\n" ); document.write( "cosine theta is negative in the second quadrant and in the third quadrant.
\n" ); document.write( "since the third quadrant allows tangent to be positive and cosine to be negative, your answer must be in the third quadrant.
\n" ); document.write( "the equivalent angle in the third quadrant that has the same tangent as an angle in the first quadrant would be equal to pi + 1.165542528 radians which makes the angle equal to 4.307135181 radians.
\n" ); document.write( "this is equivalent to 1.371003709 * pi radians.
\n" ); document.write( "to make this into degrees multiply by 180 and divide by pi to get 246.7806677 degrees.\r
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