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Question:

cos(156 degrees) cos(35 degrees) plus sin(156 degrees) sin(35 degrees)?

jheyson2011

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5yrs
We have the formula: cos(a - b) = cos a . cos b + sin a . sin b
Then:
cos(156 degrees) cos(35 degrees) plus sin(156 degrees) sin(35 degrees) = cos(156 degrees - 35 degrees) = cos (120 degrees) = - cos (60 degrees) = - 1/2

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Cos(156)Cos(35)+Sin(156)Sin(935)= -0.5150 Which if we round to a fraction will turn to -1/2. to solve this problem you just have to plot it in in your Graphic calculator.
P.s. Do n0t forget the (PARENTHESIS)
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we know that : cos x . cos y +sin x . sin y = cos ( x - y) .
comparing the problem with the above formula ;
we get : x = 156 degrees , y = 35 degrees
therefore,
cos(156 degrees) cos(35 degrees) plus sin(156 degrees) sin(35 degrees)
= cos(156 degrees - 35 degrees)
= cos (120 degrees)
= cos (180 degrees- 120 degrees)
= - cos (60 degrees) [ since cos in second quadrant is negative i.e from 90 degrees to 180 degrees]
= - 1/2
therefore,
cos(156 degrees) cos(35 degrees) plus sin(156 degrees) sin(35 degrees) = - 1/2 = - 0.5
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