Key to "If sin⁡(x+28∘)=cos⁡(3x−78∘), then find x"

Nylah Church

Answered question

2022-01-24

\sin (x + 28^{\circ}) = \cos (3 x - 78^{\circ})

, then find x

eris0cg

Beginner2022-01-25Added 13 answers

Remember that

\cos x = \cos α \Rightarrow x = \pm α

, so in your case:

\sin (x + 28) = \cos (90 - x - 28) = \cos (3 x - 78) \Rightarrow 62 - x = \pm (3 x - 78) \Rightarrow

\Rightarrow {\begin{matrix} 62 - x = 3 x - 78 \Rightarrow 4 x = 140 \Rightarrow x = 35 \\ or \\ 62 - x = - 3 x + 78 \Rightarrow 2 x = 16 \Rightarrow x = 8 \end{matrix}

Karlie Wilkins

Beginner2022-01-26Added 7 answers

Hint: Use

\sin (x) - \cos (y) = - 2 \sin (- \frac{x}{2} - \frac{y}{2} + \frac{π}{4}) \sin (- \frac{x}{2} + \frac{y}{2} + \frac{π}{4})

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