Thread: Find all solutions in the interval..........

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

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

Originally Posted by sweetG

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

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

Hello,

The writing means

Remember the identity :

The equation is now :







Solve the final

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 >_<

Originally Posted by sweetG

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 >_<

Yes, you are correct for the range provided.

The function has a period of . If no range was provided, then there would be infinite solution, some of which could be:

Originally Posted by sweetG

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 >_<

That's good

From the final equation, you have that cos(x)-1/2=0, that is to say cos(x)=1/2

According to the unit circle there are only 2 values of x that satisfy this, between -180 and 180 (complete turn). It's ok

Thanks Moo and Air
It makes a lot more sense now