Use Sum or Difference of angles to find the exact values: sin195 degrees?

answer must be in simplified radical form.

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  • 1 decade ago
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    To find sin 195º exactly, we first notice that 195º = 180º + 15º = π + π/12. Next, we use the fact that sin (α + π) = -sin α, since sin (α + π) = sinα∗cosπ + cosπ∗sinα = 0 + (-1)∗sinα = -sinα.

    In our problem, we have α = π/12, and π/12 = π/3 - π/4.

    So, noting that sin(π/3) = √3/2, sin(π/4) = √2/2, cos(π/3) = 1/2, cos(π/4) = √2/2, we get:

     sin 195º = sin(π + π/12)

                  = - sin(π/12)

                  = - sin(π/3 - π/4)

                  = - [sin(π/3)∗cos(π/4) - cos(π/3)∗sin(π/4)]

                  = - [√3/2∗√2/2 - 1/2∗√2/2]

                  = - [√6 - √2]/4

                  =   [√2 - √6]/4 ∆

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