Processing Math: Done

From Förberedande kurs i matematik 1

We can write the expression sinx+y  in terms of sin x, cos x, sin y and cos y if we use the addition formula for sine,

sinx+y=sinxcosy+cosxsiny 

In turn, it is possible to express the factors cos x and cos y in terms of sin x and sin y by using the Pythagorean identity,

cosx=1−sin2x=1−232=35cosy=1−sin2y=1−132=322

Because x and y are angles in the first quadrant, cos x and cos y are positive, so we in fact have

cosx=35  and cosy=322 

Finally, we obtain

sinx+y=32322+3531=942+5