Trigonometry

posted by Brandi

If cos(a)=1/2 and sin(b)=2/3, find sin(a+b), if

1) Both angles are acute; Answer: (sqrt(15)+2)/6
ii) a is an acute angle and pi/2 < b < pi; Answer: (2-sqrt(15))/6

2. Find the exact value of the six trigonometric functions of 13pi/12.
Partial answer: cos(13pi/12)=-(sqrt(6)+sqrt(2))/4

  1. Steve

    13/12 = 5/4 - 1/6
    sin 5pi/4 = -1/√2
    cos 5pi/4 = -1/√2
    sin pi/6 = 1/2
    cos pi/6 = √3/2
    so,
    sin(13pi/12) = sin(5pi/4 - pi/6) = (-1/√2)(√3/2)-(-1/√2)(1/2) = (1-√3)/√8
    and so on for the others

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