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Solution 4.3:7b

From Förberedande kurs i matematik 1

Revision as of 10:29, 30 September 2008 by Ian (Talk | contribs)
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Using the addition formula, we rewrite sinx+y  as


sinx+y=sinxcosy+cosxsiny 


If we use the same solution procedure as in exercise a, we use the Pythagorean identity

cos2v+sin2v=1 to express the unknown factors x and y in terms of cos x and cos y,

sinx=1−cos2x=1−522=1−425=521siny=1−cos2y=1−532=1−925=54 


The angles x and y lie in the first quadrant and both sin x and sin y are therefore positive, i.e.


sinx=521  and siny=54


Thus, the answer is


sinx+y=52153+5254=25321+8 

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