Solve for x sin(3x+13)=cos(4x)

Problem

sin(3*x+13)=cos(4*x)

Solution

1. Apply the cofunction identity to express the cosine function in terms of sine using the relationship cos(θ)=sin(90−θ)

sin(3*x+13)=sin(90−4*x)

2. Set up the first general solution by equating the arguments of the sine functions, adding the periodic constant 360*k where k is an integer.

3*x+13=90−4*x+360*k

3. Solve for x in the first case by combining like terms and isolating the variable.

7*x=77+360*k

x=11+(360*k)/7

4. Set up the second general solution using the identity sin(θ)=sin(180−θ)

3*x+13=180−(90−4*x)+360*k

5. Simplify and solve for x in the second case.

3*x+13=90+4*x+360*k

−x=77+360*k

x=−77−360*k

Final Answer

x=11+(360*k)/7* or *x=−77+360*k

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