document.write( "Question 818283: \"compute the exact values of sin 2x, cos 2x, tan 2x without a calculator. Cos x= (-4/5), pi/2\n" ); document.write( "\n" ); document.write( "So far I have figured out that I need to use the identities sin 2x= 2sin x cos x, cos 2x=cos^2 x - sin^2 x
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Algebra.Com's Answer #492464 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
\"compute the exact values of sin(2θ), cos(2θ), tan(2θ) without a calculator.
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document.write( " cos(θ)=,  < θ < .\r\n" );
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document.write( "I changed your x's to θ so that x could represent the values on the\r\n" );
document.write( "x-axis rather than the angle.\r\n" );
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document.write( "We draw the angle θ in the second quadrant.\r\n" );
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document.write( "And we draw a perpendicular to the x-axis from the end of the green line\r\n" );
document.write( "forming a right triangle.\r\n" );
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document.write( "The bottom side of the triangle is x\r\n" );
document.write( "The vertical side of the triangle is y, \r\n" );
document.write( "and the green line is r.\r\n" );
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document.write( "The cosine is  and we are given that  cos(θ)=\r\n" );
document.write( "so we will take x as the numerator, considering it negative, since it\r\n" );
document.write( "goes to the left.  So we will label it x=-4, and we will label r as\r\n" );
document.write( "the denominator of , considering it positive, since it goes\r\n" );
document.write( "up.  So we will label it as r=5\r\n" );
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document.write( "We calculate y from\r\n" );
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document.write( "r² = x²+y²\r\n" );
document.write( "5² = (-4)²+y²\r\n" );
document.write( "25 = 16+y²\r\n" );
document.write( " 9 = y²\r\n" );
document.write( "±3 = y, we take the positive value since y goes up.\r\n" );
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document.write( "So we label the y-value as 3\r\n" );
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document.write( "sin(2θ) = 2sin(θ )cos(θ ) \r\n" );
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document.write( "Since sin(θ ) = , sin(θ ) =   \r\n" );
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document.write( "sin(2θ) = 2sin(θ )cos(θ ) = 2 = \r\n" );
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document.write( "cos(2θ) = cos²(θ)-sin²(θ) = - = - =  \r\n" );
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document.write( "tan(2θ) =  \r\n" );
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document.write( "Since the tangent is , tan(θ) =  = \r\n" );
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document.write( "tan(2θ) =  =  \r\n" );
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document.write( "Multiply top and bottom by 16\r\n" );
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document.write( "tan(2θ) =  =  =  = \r\n" );
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document.write( "Edwin

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