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The only question that I can see to make sense is:

Solve x for: cos(5x + 49°) = sin(3x + 57°)

It's been a while since I did this kind of problem, so there may be more solutions to the ones I give here:

Cosθ = sin(90 - θ)

→ cos(5x + 49°) = sin(3x + 57°)

→ sin(90° - (5x + 49°)) = sin(3x + 57°)

→ sin(41° - 5x) = sin(3x + 57°)

Thus:

41° - 5x = 3x + 57°

→ 8x = -16°

→ x = -2°

But as sin and cos are cyclic with a period of 360°, -2° = 360° - 2= 358°

→ x = 358° + 360°n where n = 0, 1, 2, ....

But sin θ = sin(180° - θ) which means that

180 - (41° - 5x) = 3x + 57°

→ 5x + 139° = 3x + 57°

→ 2x = -82°

→ x = -41°

→ x = 319° + 360°n where n = 0, 1, 2, 3,... is also a solution set.

Thus the solutions are:

x = 358° + 360°n

x = 319° + 360°n

where n = 0, 1, 2, 3, ...

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8y ago

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