Minimum value of \(\displaystyle{h}{\left(\theta\right)}={3}{\sin{\theta}}-{4}{\cos{\theta}}+\sqrt{{{2}}}\) Find the minimum value

Ean Hughes

Ean Hughes

Answered question

2022-04-14

Minimum value of h(θ)=3sinθ4cosθ+2
Find the minimum value of h(θ)
h(θ)=3sinθ4cosθ+2=5sin(θ+53.13)+2
Minimum value - 5sin(θ+53.13)+2=5
Therefore min value is = 552
Why am I wrong ?

Answer & Explanation

Drantumcem0

Drantumcem0

Beginner2022-04-15Added 10 answers

Minimum is attained when sin(θ+53.13)=1 that is
hmin=h(3π2+kπ)=5sin(3π2+kπ)+2=5+2
for the same reason the maximum is attained when sin(θ+53.13)=1

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