Solve the equation sin^2x - sqroot2 cosx = cos^2x + sqroot2 cosx + 2 for x in the interval 0 to 2pi

Question

Solve the equation sin^2x - sqroot2 cosx = cos^2x +  sqroot2 cosx + 2 for x in the interval 0 to 2pi

campbell_st · Answer

well use the trig identity

$$\sin^2(x) + \cos^2(x) = 1$$

make sin^2(x) the subject and then substitute into the left hand side of the equation..

then you'll end up with a quadratic equation after collecting like terms.. 

just solve the quadratic

anonymous · Answer

So would it simplify to $$2\cos^2(x) + 2\sqrt{2} \cos(x)+1=0$$?

campbell_st · Answer

yep....thats it... I'd use the general quadratic formula now to find cos(x) and then you can find x

anonymous · Answer

but in the quadratic equation it becomes $$\frac{-2\sqrt{2}\pm \sqrt{0}}{4}$$

campbell_st · Answer

yep so 

$$\cos(x) = \frac{-\sqrt{2}}{2}$$

which is think is 2nd and 3rd quadrants.... 3/4 pi  and 5/4 pi

anonymous · Answer

Ohhh that makes sense. Thank you so much! :) Putting it into the calculator confused me.

campbell_st · Answer

lol... it can be like that... well done...