(a)
T(m) = −22.75 cosπ/6(m − 1) + 52.55 = 48
m =
−22.75 cos (π/6(m − 1)) + 52.55 = 48
-22.75 cos ((π/6)(m-1)) = -4.55
cos ((π/6)(m-1)) = .2
((π/6)(m-1)) = 1.369438... or ((π/6)(m-1)) = 4.9137459..
m-1 = 2.61543.. or m-1 = 9.38456..
m = 3.615435 or m = 10.38457
adding/subtracting 2π to each answer will produce a new answer.
To solve the equation T(m) = -22.75 cos(π/6(m - 1)) + 52.55 = 48, you need to isolate the variable m.
First, subtract 52.55 from both sides of the equation:
-22.75 cos(π/6(m - 1)) = 48 - 52.55
-22.75 cos(π/6(m - 1)) = -4.55
Now, divide both sides of the equation by -22.75 to isolate the cosine term:
cos(π/6(m - 1)) = -4.55 / -22.75
cos(π/6(m - 1)) = 0.2
To find the value of m, you need to take the inverse cosine (or arccos) of both sides of the equation. This will give you the angle whose cosine is 0.2:
π/6(m - 1) = arccos(0.2)
To solve for m, multiply both sides of the equation by 6/π:
m - 1 = (6/π) * arccos(0.2)
Finally, add 1 to both sides of the equation to obtain the value of m:
m = 1 + (6/π) * arccos(0.2)
Using a calculator, you can find the numerical value of arccos(0.2). Substitute this value into the equation to find the specific value of m.