Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

Find cos(s+t) and cos(s-t)?

Given : Cos s= -8/17 & cos t=-3/5 & s and t are in quadrant 3

1 Answer

Relevance
  • Raj K
    Lv 7
    9 years ago
    Favorite Answer

    Find cos(s+t) and cos(s-t)?

    Given : Cos s= -8/17 & cos t=-3/5 & s and t are in quadrant 3

    Now cos(s) = −8/17

    sin(s) =±√ {1−cos²(s)}

    =±√ {1−(−8/17)²}=±√ {1−64/289}=±√ {225/289}=±15/17

    Rejecting + sign because s is in third quadrant

    Hence sin(s)=−15/17

    Also cos(t) = −3/5

    sin(s) =±√ {1−cos²(s)}

    =±√ {1−(−3/5)²}=±√ {1−9/25}=±√ {16/25}=±4/5

    Rejecting + sign because t is in third quadrant

    Hence sin(t)=−4/5

    cos(s+t)=cos(s)cos(t)−sin(s)sin(t)

    =(−8/17)×(−3/5)−{(−15/17)×(−4/5)}

    =24/85−60/85 = −36/85

    Again

    cos(s−t)=cos(s)cos(t)+sin(s)sin(t)

    =(−8/17)×(−3/5)+{(−15/17)×(−4/5)}

    =24/85+60/85 =84/85

Still have questions? Get your answers by asking now.