Find minimum value of \(\displaystyle{8}{\cos{{x}}}+{4}{\sin{{x}}}\) and corresponding

Ariel Collier

Ariel Collier

Answered question

2022-04-14

Find minimum value of 8cosx+4sinx and corresponding value of x
I used the R method to simplify it -
80cos(x26.565)
Minimum value of that =
80cos(x26.565)=80
cos(x26.565)=1
This cosine value lies in the 2nd and 3rd quadrant
letting x-26.565=y
y reference angle =cos1(1)=180
2nd quadrant - 180-y(ref)=0
3rd quadrant - 180+y(ref)=360
Therefore , x=26.565,386.565
Why am I wrong ? The minimum value is 206.6

Answer & Explanation

YAMAGAMA699k

YAMAGAMA699k

Beginner2022-04-15Added 8 answers

Your method is perfectly fine, you just made a mistake at the end.
cos(u)=1u180°(mod 360)
Here u=xx0 so you should get x180°+x0(mod360)
Applying to x0=26.565 you get x=206.565

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