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Question:

pavelpimen
pavelpimen
Student
High School - 10th Grade

Calculate cos (23pi/12) *sin(pi/12)

 

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Posted by pavelpimen on Monday June 22, 2009 at 4:21 AM and tagged with cosine, math, sine.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    By trigonometry we know:

    Sin(A+B)-sin(A-B)=2cosAcosB    or

    cosAcosB=(1/2){sin(A+B)-sin(A-B)}. We use this to simplify the given exprssion:

     

    Cos(23Pi/12)sin2(pi/12) = (1/2){ sin(23pi/12 + pi/12)-sin(23pi/12 -pi/12)}

    =(1/2)sin((23pi+pi)/12) - (1/2)sin(22pi/12)

    =(1/2)sin(2pi)-(1/2)sin (24pi- 2pi)/12

    =(1/2)sin(0)-(1/2)sin(2pi-pi/6),  as sin (2pi) =sin (0) = 0.

    =(1/2)(0)  -(1/2)sin(-pi/6),   as sin(-A) = -sin(A)

    =0   -(1/2) (-sin(pi/6)

    =(1/2)sin(pi/6) = 1/2(1/2) =1/4

     

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    Posted by neela on Monday June 22, 2009 at 7:11 AM