CALCULUS ONE!

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The graph of sinx and cosx intersect once between 0 and pi/2. What is the angle between the two curves at the point where they intersect? (You need to think about how the angle between two curves should be defined).

  • CALCULUS ONE! -

    first find their intersection

    sinx = cosx
    sinx/cosx = 1
    tanx = 1
    x = 45° or π/4 radians

    for y = sinx , dy/dx = cosx
    so at x = π/4 , dy/dx = 1/√2
    tan^-1(1/√2) = 35.26°

    for y = cosx , dy/dx = -sinx
    so at x = π/4 , dy/dx = -1/√2
    tan^-1(-1/√2) = 144.74°

    angle between the two tangents = 144.74 - 35.26 = 109.48°

    set your calculator to radians if you need your answer in radians.

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