Solving equations in Trigonometry

Question

Find the value of 𝜃, when sin(8𝜃)cos(4𝜃)=0

Answer 1

The solutions will be given by sin 8x=0 or cos 4x = 0.

x=0, π/8

These are solution between 0 and 2π...but there will be other solutions.

Answer 2

Assuming that we are working in degrees....

The sine of an angle goes to 0 when the angle is 0 + 180*n (in other words, every 180 degrees, starting at 0.

So, if we have 8*θ, the 0 comes when θ = 0 + (180/8)*n. (Every 22.5 degrees, starting at 0.)

Using similar logic, the cosine of 4*θ goes to 0 every 45 degrees, starting at 22.5

So, you can see that the product is 0 for many different combinations