Recall that sine and cosine are co-functions. That means they satisfy the equation
[tex]\sin x = \cos(90-x)[/tex]
For example, sin 30° = cos 60°. Now, using this property, we have
[tex]\sin(3x + 13) = \cos[90 - (3x + 13)][/tex]
As can be seen from the equation provided, it shows that sin(3x + 13) = cos(4x). This means that the left-hand side of the equations are equivalent. Thus, we have
90 - (3x + 13) = 4x
90 - 3x - 13 = 4x
77 = 7x
x = 11
We now have the value of x. We can also check if we got the right answer by substituting the value into the original equation.
Answer: 11
