Find x and y such that 15 sin &#x2061;<!-- ⁡ --> ( x + y ) + 7 sin

Kendall Oneill

Kendall Oneill

Answered question

2022-05-12

Find x and y such that 15 sin ( x + y ) + 7 sin x + 7 sin y is maximized
What I tried was
f ( x , y ) = 15 sin ( x + y ) + 7 sin x + 7 sin y = 15 ( sin x cos y + cos x sin y ) + 7 ( sin x + sin y )
f x = 15 cos ( x + y ) + 7 cos x = 0
f y = 15 cos ( x + y ) + 7 cos y = 0
cos x = cos y

Answer & Explanation

oedfeuonbk203

oedfeuonbk203

Beginner2022-05-13Added 15 answers

Hint:
Observe that
f x = 0 = f y cos x = cos y x = 2 n π ± y for some  n Z
If x = 2 n π + y we have
f x = 0 15 cos ( 2 n π + 2 y ) + 7 cos ( 2 n π + y ) = 0 15 cos ( 2 y ) + 7 cos y = 0 15 ( 2 cos 2 y 1 ) + 7 cos y = 0 30 cos 2 y + 7 cos y 15 = 0 cos y { 3 5 , 5 6 }

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