Find all solutions in the interval-180o ≤ x ≤ 180o

to the equation cosx + (sin^2)x = 5/4

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- Jul 16th 2008, 06:14 AMsweetGFind all solutions in the interval..........
**Find all solutions in the interval**-180o ≤ x ≤ 180o

**to the equation cosx + (sin^2)x = 5/4**

- Jul 16th 2008, 07:19 AMMoo
Hello,

The writing $\displaystyle \sin^2 x$ means $\displaystyle (\sin(x))^2$ ;)

Remember the identity : $\displaystyle \cos^2(x)+\sin^2(x)=1 \implies \sin^2(x)=1-\cos^2(x)$

The equation is now :

$\displaystyle \cos x+1-\cos^2 x=\tfrac 54$

$\displaystyle \cos^2 x-\cos x+\tfrac 14=0$

$\displaystyle (\cos(x)-\tfrac 12)^2=0$

Solve the final :p - Jul 18th 2008, 07:22 AMsweetG
Does that mean x will equal 60 and - 60 ?

Is that right and are there any more solutions ?

I've forgotten how to do these types of questions >_< - Jul 18th 2008, 10:40 AMSimplicity
- Jul 18th 2008, 10:40 AMMoo
- Jul 19th 2008, 07:26 AMsweetG
Thanks Moo and Air :)

It makes a lot more sense now