Monday, September 21, 2015

trigonometry How calculate cos of 165 (sum or difference of what angles)? cos(165)

We need to find
the values of cos(165).

We will need to rewrite the number (165) as a sum of
two known angles.

165 = 210 - 45   (210 is the angle 30 in the third
quadrant).

==> cos(165) = cos(210 - 45)

Now we will use
trigonometric identities to solve.

cos(210 - 45) = cos210*cos45 +
sin210*sin45

                     = -sqrt3/2 * sqrt2/2 +
(-1/2)*(sqrt2/2)

                     = -sqrt6/ 4 - sqrt2 /4


                     = (-sqrt6 - sqrt2)/4

                      =
-sqrt2(sqrt3 +1) /4

==> cos(165) = -sqrt2(sqrt3  +1) /
4

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