How to solve sin &#x2061;<!-- ⁡ -->

Aedan Tyler

Aedan Tyler

Answered question

2022-05-17

How to solve sin ( x ) + 2 2 cos x = 3

Answer & Explanation

Lilia Randall

Lilia Randall

Beginner2022-05-18Added 14 answers

Your problem is of the following form
a sin x + b cos x = c
where a=1, b = 2 2 and c=3.
Let R = a 2 + b 2 </math. We can define
A = a R = cos θ
and
B = b R = sin θ
Therefore
a sin x + b cos x = R ( A sin x + B cos x ) = R ( cos θ sin x + sin θ cos x ) = R sin ( x + θ ) .
Hence
sin ( x + θ ) = c R
or
x = ( sin 1 c R ) θ = ( sin 1 c R ) ( sin 1 b R ) = ( sin 1 3 3 ) ( sin 1 2 2 3 ) = 0.3398

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