Answer:
b ∈ (3.5, 4]
Step-by-step explanation:
You want the range of b, given cos(a) = b -3 and a ∈ (-60°, 60°).
Cosine
The cosine function is an even function (symmetrical about the y-axis) that is decreasing on the interval (0, 180°). It has a maximum value of 1 at θ = 0.
Range
Solving for b, we have ...
cos(a) = b -3
b = 3 +cos(a)
The discussion above tells us ...
b = 3 +cos(0) = 3 +1 = 4 . . . . . the maximum value of b
b = 3 +cos(60°) = 3 +1/2 = 3.5 . . . . . the minimum value of b (limit)
That is, the values of b will range from 3.5 to 4, with the value 3.5 being the limit of the range, and not actually included in the range.
b ∈ (3.5, 4]
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Additional comment
The attached graph shows 'b' versus 'a' using radian measure for the angles. 60° = π/3 radians.
