cos(56°-3x)=-0.785

where 0° ≤ x ≤ 360°

cosine is an even function $\implies \cos(56-3x) = \cos(3x-56)$

$0 \le x < 360 \implies 0 \le 3x < 1080 \implies -56 \le 3x-56 < 1024$

let $u=3x-56$. $\cos{u} = -0.785 \implies u$ is an angle residing in quadrants II or III

Quad II angles ...$u = \arccos(-0.785) \approx 141.72$ and the additional coterminal angles $501.72$ and $861.72$

$3x-56= \{141.72,501.72,861.72 \} \implies x \in \{65.9, 185.9, 305.9 \}$

Quad III angles ... $u = 360 - \arccos(-0.785) \approx 218.28$ and the additional coterminal angles $578.28$ and $938.28$

$3x-56= \{218.28,578.28,938.28 \} \implies x \in \{91.43, 211,43, 331.43 \}$