Here's another question I'm in need of help with for my homework. Find the EXACT expressions for the indicated quantities, given that:?

Cos(pie/12)=(√2+√ 3)/(2) & Sin(pie/8)=(√2−√2)/(2)

cos (π /8)

sin π /12 

tan π /12

cos 25π /12

2 Answers

Relevance
  • 2 months ago

    a) sin²(π/8) + cos²(π/8) = 1

    so, cos²(π/8) = 1 - sin²(π/8)

    Hence, cos(π/8) =  √[1 - sin²(π/8)]

    b) Also, sin²(π/12) + cos²(π/12) = 1

    so, sin²(π/12) = 1 - cos²(π/12)

    Hence, sin(π/12) = √[1 - cos²(π/12)]

    so, given values of sin(π/8) and cos(π/12) these can be evaluated.

    Sadly, your values are not correct.

    In fact, cos(π/12) = (√6+√2)/4 and sin(π/8) = 0.3827

    c) Then, tan(π/12) = sin(π/12)/cos(π/12)

    d) And, cos(25π/12) => cos(2π + (π/12)) = cos(π/12)

    :)>

  • ted s
    Lv 7
    2 months ago

    since NEITHER cos (π / 12 ) and sin (π / 8 ) have the correct {valid } values...and it is ' pi ' , not ' pie'....then you cannot answer these with the given information

    sin π/12 = sin ( π / 3 - π / 4) = sin π / 3 cos π / 4 - cos π / 3 sin π / 4 &

    cos 25π / 12 = cos π / 12  = cos π / 3 cos π / 4 + sin π / 3 sin π / 4 &

    tan π / 12 = sin π / 12   / cos π /12 ...these 3 should be easy

    finally cos π / 8 = 2 cos² π / 4 - 1 so this is also attainable

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