Find all solutions in the interval -180o ≤ x ≤ 180o to the equation cosx + (sin^2)x = 5/4
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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
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