(3cos2(x))+cos(x)+2=0

Question

find to the nearest degree, all values of x in the interval 0<360 that satify the equation

Answer 1

3cos(2x) + cos(x) + 2 = 0 can be simplified to

 

3(cos(x)cos(x)-sin(x)sin(x)) + cos(x) + 2 = 0 using the double angle formula for cosine

 

This simplifies to 

 

3(2cos(x)cos(x)-1) + cos(x) + 2 = 0 using sin(x)sin(x)+cos(x)cos(x) = 1

 

Simplifying this further will yield

 

6cos(x)cos(x) + cos(x) -1 = 0 

 

Let y = cos(x). Now solve 6y^2 + y - 1 = 0 using the quadratic formula. You should be able to take it from there.