Answer:
a. {0.322, 1.571, 3.463, 4.712}
b. {π/6, 5π/6, 7π/6, 11π/6}
Step-by-step explanation:
These equations can be solved by factoring and making use of the zero product rule.
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5a.
3cos(x) -cot(x)cos(x) = 0
cos(x)(3 -cot(x)) = 0 . . . . factored
Has solutions ...
cos(x) = 0 ⇒ x = π/2, 3π/2 or {1.571, 4.712}
3 -cot(x) = 0 ⇒ x = arctan(1/3) +nπ ≈ {0.322, 3.463}
The solutions are ...
x ∈ {0.322, 1.571, 3.463, 4.712}
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5b.
3sec²(x) -4 = 0
(√3sec(x) -2)(√3sec(x) +2) = 0 . . . . factored
Has solutions ...
√3sec(x) -2 = 0 ⇒ cos(x) = √3/2 ⇒ x = π/6, 11π/6
√3sec(x) +2 = 0 ⇒ cos(x) = -√3/2 ⇒ x = 5π/6, 7π/6
x ∈ {π/6, 5π/6, 7π/6, 11π/6}
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Additional comment
The equations are already in a form such that the solutions are the x-intercepts of the function on the left side of the equal sign. A graphing calculator finds those easily.
