solve the equation 4cos^2(x) -15sin(x) = 13

We first want to get every term in terms of the same variable, namely sin(x). to do so, we will use the identity sin^2(x) +cos^2(x) = 1 to get: 4(1-sin^2(x)) -15sin(x) -13 = 0. which we can then rewrite as: 4sin^2(x) +15sin(x)+9=0 and solve it as a quadratic equation in sin(x), giving us: (4sin(x)+3)(sinx+3)=0. Hence x = arcsin(-3/4) or arcsin(-3), Of which only x = arcsin(-3/4) is a valid solution.