SOLUTION: tan &#946; = 2, 180° < &#946; < 270°. Find the exact value of sin 2&#946; and cos 2&#946;

Algebra ->  Trigonometry-basics -> SOLUTION: tan &#946; = 2, 180° < &#946; < 270°. Find the exact value of sin 2&#946; and cos 2&#946;      Log On


   

Question 867728: tan β = 2, 180° < β < 270°. Find the exact value of sin 2β and cos 2β
Answer by lwsshak3(11628) About Me  (Show Source):
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tan β = 2, 180° < β < 270°. Find the exact value of sin 2β and cos 2β
hypotenuse of reference right triangle=sqrt%282%5E2%2B1%5E2%29=sqrt%284%2B1%29=sqrt%285%29
cos%28beta%29=-1%2Fsqrt%285%29
sin%28beta%29=-2%2Fsqrt%285%29

cos%282beta%29=cos%5E2%28beta%29-sin%5E2%28beta%29=1%2F5-4%2F5=-3%2F5
..
Calculator check:
tan(B)=2
B=243.435(in quadrant III)
2B≈486.87(in quadrant II)
sin(2B)=sin(486.87)≈0.7999…
Exact value as calculated=4/5=0.8000
cos(2B)=cos(486.87≈-0.6000…
Exact value as calculated=-3/5=-0.6000