Plug all the point into your calculator. Not sure if you need it y=mx+b but the R for that is r= -1
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Solve the trigonometric equation:
![\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B2%5C%2Ccos%5E2%5C%2Cx-cos%5C%2Cx%3D1%7D%5C%5C%5C%5C%20%5Cmathsf%7B2%5C%2Ccos%5E2%5C%2Cx-cos%5C%2Cx-1%3D0%7D)
Make a substitution:
![\mathsf{cos\,x=t\qquad (-1\le t\le 1)}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2Cx%3Dt%5Cqquad%20%28-1%5Cle%20t%5Cle%201%29%7D)
and the equation becomes
![\mathsf{2t^2-t-1=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B2t%5E2-t-1%3D0%7D)
Rewrite conveniently
– t as
+ t – 2t, and then factor the left-hand side by grouping:
![\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B2t%5E2%2Bt-2t-1%3D0%7D%5C%5C%5C%5C%20%5Cmathsf%7Bt%5Ccdot%20%282t%2B1%29-1%5Ccdot%20%282t%2B1%29%3D0%7D)
Factor out
2t + 1:
![\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}](https://tex.z-dn.net/?f=%5Cmathsf%7B%282t%2B1%29%5Ccdot%20%28t-1%29%3D0%7D%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Brcl%7D%20%5Cmathsf%7B2t%2B1%3D0%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bt-1%3D0%7D%5C%5C%5C%5C%20%5Cmathsf%7B2t%3D1%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bt%3D1%7D%5C%5C%5C%5C%20%5Cmathsf%7Bt%3D%5Cdfrac%7B%5C%2C1%5C%2C%7D%7B2%7D%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bt%3D1%7D%20%5Cend%7Barray%7D)
Substitute back for
t = cos x:
![\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Cmathsf%7Bcos%5C%2Cx%3D%5Cdfrac%7B%5C%2C1%5C%2C%7D%7B2%7D%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bcos%5C%2Cx%3D1%7D%5C%5C%5C%5C%20%5Cmathsf%7Bcos%5C%2Cx%3Dcos%5C%2C60%5E%5Ccirc%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bcos%5C%2Cx%3Dcos%5C%2C0%7D%20%5Cend%7Barray%7D)
Therefore,
![\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%20%5Cmathsf%7Bx%3D%5Cpm%5C%2C60%5E%5Ccirc%2Bk%5Ccdot%20360%5E%5Ccirc%7D%26~%5Ctextsf%7B%20or%20%7D~%26%5Cmathsf%7Bcos%5C%2Cx%3D0%2Bk%5Ccdot%20360%5E%5Ccirc%7D%20%5Cend%7Barray%7D)
where
k is an integer.
Solution set:
![\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}](https://tex.z-dn.net/?f=%5Cmathsf%7BS%3D%5Cleft%5C%7Bx%5Cin%5Cmathbb%7BR%7D%3A~~x%3D-%5C%2C60%5E%5Ccirc%2Bk%5Ccdot%20360%5E%5Ccirc~~or~~x%3D60%5E%5Ccirc%2Bk%5Ccdot%20360%5E%5Ccirc~~or~~x%3Dk%5Ccdot%20360%5E%5Ccirc%2C~~k%5Cin%5Cmathbb%7BZ%7D%5Cright%5C%7D%7D)
I hope this helps. =)
Answer:
Step-by-step explanation:
24 hours---------->1 day
x hours------------>6 days
Cross multiplying:
x=24x6
x=144 hrs
Answer:
ill guess -2 for u
Step-by-step explanation: