Question
What are all values of e, 0leqslant Theta leqslant 2pi for which (sin^2Theta )(2cosTheta -sqrt (2))geqslant 0 Select all that apply.
Answer
4
(173 Votes)
Aiden
Veteran · Tutor for 11 years
Answer
The values of
that satisfy the inequality are in the intervals [0, π/4] and [7π/4, 2π], and the individual solutions are 0, π/4, and 2π.
Explanation
## Step1The given inequality is:
To find the solution set, we need to find the values of
for which the expression is equal to zero.## Step2The expression will be zero when either
or
.## Step3For
, the solutions are
.## Step4For
, the solution is
.## Step5These solutions split the interval [0, 2π] into five intervals: [0, π/4], (π/4, π), (π, 7π/4), (7π/4, 2π).## Step6We can test each interval to see whether the inequality holds.## Step7For
in [0, π/4], the expression is always ≥ 0.## Step8For
in (π/4, π), the expression is always ≤ 0.## Step9For
in (π, 7π/4), the expression is always ≤ 0.## Step10For
in (7π/4, 2π), the expression is always ≥ 0.## Step11Also, the solutions are
.