Trigonometric inequalities and graph transformations
Answers are for parents and teachers.
1
Solve sin x ≥ 1/2 (general form).
x ∈ [π/6 + 2πk, 5π/6 + 2πk], k ∈ ℤ
2
Solve cos x < 0 on [0, 2π].
(π/2, 3π/2)
3
Solve tan x > −1 on (−π/2, π/2).
(−π/4, π/2)
4
Describe how to obtain y = −(x − 2)² + 3 from y = x². Find the vertex.
Shift 2 units right, reflect in Ox, raise by 3 units; the vertex is (2, 3).
5
How is y = 2 sin 3x − 1 obtained from y = sin x? State the amplitude, period and midline.
Ordinates stretched 2 times, abscissas compressed 3 times, shifted 1 unit down; amplitude 2, period 2π/3, midline y = −1.