Answer:
[tex]m = 6[/tex]
Step-by-step explanation:
[tex]T = -15cos(\frac{\pi m}{6}) +61[/tex]
[tex]76 = -15cos(\frac{\pi m}{6}) +61[/tex]
[tex]76-61 = -15cos(\frac{\pi m}{6})[/tex]
[tex]15 = -15cos(\frac{\pi m}{6})[/tex]
[tex]\frac{15}{-15} = cos(\frac{\pi m}{6})[/tex]
[tex]-1 = cos(\frac{\pi m}{6})[/tex]
[tex]cos^{-1}( -1) = \frac{\pi m}{6}[/tex]
[tex]\pi = \frac{\pi m}{6}[/tex]
[tex]6\pi = \pi m[/tex]
[tex]m = 6[/tex]
