Question

Find a possible solution to the equation sin(3x+13)=cos(4x)

Answer 1

Recall that sine and cosine are co-functions. That means they satisfy the equation

$\sin x = \cos(90-x)$

For example, sin 30° = cos 60°. Now, using this property, we have

$\sin(3x + 13) = \cos[90 - (3x + 13)]$

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