Finding the range of p such that

Reagan Gomez

Reagan Gomez

Answered question

2022-04-08

Finding the range of p such that p=3cos2x+4sinx

Answer & Explanation

Frain4i62

Frain4i62

Beginner2022-04-09Added 16 answers

Step 1
We have 3(1sin2x)+4sin{x}=p
or sin2x43sin{x}=1p3
or (sin{x}23)2=133p9,
Step 2
which gives firstly
p133.
The equality occurs for sinx=23, which says that we got a maximal value.
Step 3
Also, p(sin{x})=3sin2x+4sin{x}+3 is a concave function, which says that p gets a minimal value for an extreme value of sin, which happens for sinx=1 or for sinx=1.
p(1)=4 and p(1)=4 and since p is a continuous function we got the answer:
[4,133]

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