document.write( "Question 825900: If tanθ = 5/12 and sinθ < 0 , evaluate
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Algebra.Com's Answer #497702 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "If tanθ = 5/12 and sinθ < 0 , evaluate \r\n" );
document.write( "a) sinθ\r\n" );
document.write( "b) cosθ\r\n" );
document.write( "c) cotθ\r\n" );
document.write( "d) secθ\r\n" );
document.write( "e) cscθ \r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Let θ be the measure the acute angle A in the right triangle ABC.\r\n" );
document.write( "Let c be the length of the hypotenuse.\r\n" );
document.write( "Let x be the length of the leg adjacent to angle A.\r\n" );
document.write( "Let y be the length of the leg opposite angle A. \r\n" );
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document.write( "a) Find sinθ\r\n" );
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document.write( "We are given tanθ = 5/12.\r\n" );
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document.write( "By definition tanθ is the ratio of the side opposite to the side adjacent, or y/x=5/12. \r\n" );
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document.write( "We can use the Pythagorean Equation to find the length of the hypotenuse c when side lengths \r\n" );
document.write( "are exactly 5 and 12. The ratios will be the same for any right triangle with acute \r\n" );
document.write( "angle θ because they will be similar triangles. \r\n" );
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document.write( "5^2 + 12^2 = c^2\r\n" );
document.write( "c^2 = 25 + 144\r\n" );
document.write( "c^2 = 169\r\n" );
document.write( "c = 13\r\n" );
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document.write( "Recall that we have the constraint that sinθ<0. Since tanθ is positive and sinθ is negative, this \r\n" );
document.write( "corresponds to an angle in Quadrant III (x<0. y<0) of the unit circle. We need to adjust signs for the trig functions accordingly.\r\n" );
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document.write( "x = -12\r\n" );
document.write( "y=-5\r\n" );
document.write( "c=13\r\n" );
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document.write( "sinθ = y/c (opposite/hypotenuse)\r\n" );
document.write( "sinθ = -5/13\r\n" );
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document.write( "By similar reasoning:\r\n" );
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document.write( "b) cosθ = x/c = -12/13\r\n" );
document.write( "c) cotθ = 1/tanθ = 12/5\r\n" );
document.write( "d) secθ = 1/cosθ = -13/12\r\n" );
document.write( "e) cscθ = 1/sinθ = -12/5\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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