document.write( "Question 567705: Find the values of the six trigonometric functions of θ if the terminal side of Ɵ lies on the given line in the specified quadrant
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Algebra.Com's Answer #366671 by Edwin McCravy(20064) $\"\"$ $\"About$

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Find the values of the six trigonometric functions of θ if the terminal side of Ɵ lies on the given line in the specified quadrant
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document.write( "Let's draw the line y = x\r\n" );
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document.write( "We want to find the six trig functions of the angle θ indicated by\r\n" );
document.write( "the red arc.\r\n" );
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document.write( "Let's find a convenient point on that line in quadrant 3, the lower left quadrant.\r\n" );
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document.write( "We can avoid a fraction by choosing to find a point where x = -3, so\r\n" );
document.write( "we substitute -3 for x in\r\n" );
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document.write( "y = x\r\n" );
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document.write( "y = (-3)\r\n" );
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document.write( "y = -1\r\n" );
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document.write( "So a convenient point on that line in quadrant 3 is (-3,-1)\r\n" );
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document.write( "Draw a vertical line from that point up to the x-axis:\r\n" );
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document.write( "That forms a right triangle in quadrant 3.  Let's label the upper\r\n" );
document.write( "leg of the right triangle the same as the x-coordinate x=-3.\r\n" );
document.write( "Let's label the green vertical leg of the triangle the same as the\r\n" );
document.write( "y-coordinate y=-1. We label the hypotenuse of that triangle as r.\r\n" );
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document.write( "Next we calculate r by using the Pythagorean theorem:\r\n" );
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document.write( "r² = x² + y²\r\n" );
document.write( "r² = (-3)² + (-1)²\r\n" );
document.write( "r² = 9 + 1\r\n" );
document.write( "r² = 10\r\n" );
document.write( "r = \r\n" );
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document.write( "So we label r as \r\n" );
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document.write( "Then we remember the six trig ratios:\r\n" );
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document.write( "sin(θ) =  =  = \r\n" );
document.write( "cos(θ) =  =  = \r\n" );
document.write( "tan(θ) =  =  = \r\n" );
document.write( "sec(θ) =  =  =  \r\n" );
document.write( "csc(θ) =  =  = \r\n" );
document.write( "cot(θ) =  =  = 3\r\n" );
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document.write( "Edwin

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