Calculus

How would you begin this problem?

On a standard summer day in upstate New York, the temperature outside can be modeled using the sinusoidal equation O(t) = 11 cos (pi/12 t) + 71, where t represents the number of hours since the peak temperature for the day.

For 0 less than or equal to t less than or equal to 24, graphically determine all points in time when the outside temperature is equal to 75 degrees. Round your answer to the nearest tenth of an hour.

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  1. set 11cos(π/12 t) + 71 = 75
    cos(πt/12) = .363636...
    set your calculator to radians and take cos^-1 (.363636...) to get 1.19862779
    so πt/12 = 1.19862779 or πt/12 = 2π-1.19862779 or 5.0845575.. (the cosine is + in quads I and IV )
    t = 4.578 or t = 19.4215

    t = 4.6 or t = 19.4 to the nearest tenth of an hour

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