Solve the equation cos θ + 4 cos 2θ = 3, giving all solutions in the interval 0◦ ≤ θ ≤ 180◦ how do we solve it ? .

1 Answer
May 29, 2018

Let #x=cos theta# and remember #cos 2 theta= 2 cos ^2 theta - 1 = 2 x^2-1# so our equation becomes

#x + 4 (2x^2-1)=3 # or #x+8x^2-4=3# or #0=8x^2+x-7=(x+1)(8x-7)# so #cos theta = -1 or cos theta=7/8 # so

#theta = 180^circ +360^circ k or theta=pm text{Arc}text{cos}(7/8) + 360^circ k quad # integer #k#

and you can work out the ones in the range.