document.write( "Question 586560: find the exact values of sin2u, cos2u, and tan2u using cosu= -2/7 \n" ); document.write( "

Algebra.Com's Answer #373803 by tw23279(14) $\"\"$ $\"About$

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Do you know how to derive these formulas?
\n" ); document.write( "If you do, just apply them.
\n" ); document.write( "So sin2u = 2cosusinu (derived by using sin(u+u) = sinucosu+cosusinu)
\n" ); document.write( "and cos2u = 2cos^2u -1 (derived by using cos(u+u) = cosucosu - sinusinu)
\n" ); document.write( "However, recall that you need the y value in order to solve for sin.
\n" ); document.write( "x^2 + y^2 = r^2
\n" ); document.write( "4 + ___ = 49
\n" ); document.write( "y = square root of 45 or 3 root 5.
\n" ); document.write( "And we can use these formulas. (Also recall that if cosu= -2/7, then u must be in either quadrant II or III because x is negative in those quadrant, which means there are also two possible answer for y because y is positive in QII and negative in QIII)
\n" ); document.write( "sin2u=2(-2/7)(+ or - root45/7) = -4/7/(+ or -)root45/7 = -4/-root45 or -4/+root45 = + or -12root5 / 45
\n" ); document.write( "cos2u = 2cos^2u - 1 = 2((-2/7)^2) - 1 = 8/49 - 49/49 = -41/49
\n" ); document.write( "And by the basic trig identity: tan2u = sin2u/cos2u = -12root5 / 25 / -41/ 49 .. again the sign should be + or -. \n" ); document.write( "

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