Question 586560: find the exact values of sin2u, cos2u, and tan2u using cosu= -2/7
Answer by tw23279(14)   (Show Source):
You can put this solution on YOUR website! Do you know how to derive these formulas?
If you do, just apply them.
So sin2u = 2cosusinu (derived by using sin(u+u) = sinucosu+cosusinu)
and cos2u = 2cos^2u -1 (derived by using cos(u+u) = cosucosu - sinusinu)
However, recall that you need the y value in order to solve for sin.
x^2 + y^2 = r^2
4 + ___ = 49
y = square root of 45 or 3 root 5.
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)
sin2u=2(-2/7)(+ or - root45/7) = -4/7/(+ or -)root45/7 = -4/-root45 or -4/+root45 = + or -12root5 / 45
cos2u = 2cos^2u - 1 = 2((-2/7)^2) - 1 = 8/49 - 49/49 = -41/49
And by the basic trig identity: tan2u = sin2u/cos2u = -12root5 / 25 / -41/ 49 .. again the sign should be + or -.
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