Sine and Absolute Value

Geometry Level 2

What is the sum of the maximum and minimum values of the function y = ∣ sin ⁡ x − 5 ∣ + 6 ? y=|\sin x-5|+6?

19 22 16 11

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Mahindra Jain by Mahindra Jain

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1 solution

Prasun Biswas
Feb 19, 2014

We can see here that the function y = f ( x ) = ∣ sin ⁡ x − 5 ∣ + 6 y=f(x)=|\sin x -5| + 6 gives max and min value on value of sin ⁡ x \sin x being on the extremes, i.e, sin ⁡ x = 1 \sin x = 1 and sin ⁡ x = ( − 1 ) \sin x = (-1)

So, Max. value of y = ∣ sin ⁡ x − 5 ∣ + 6 = ∣ − 1 − 5 ∣ + 6 = ∣ − 6 ∣ + 6 = 6 + 6 = 12 y=|\sin x -5|+6=|-1-5|+6=|-6|+6=6+6=\boxed{12}

Also, Min value of y = ∣ sin ⁡ x − 5 ∣ + 6 = ∣ 1 − 5 ∣ + 6 = ∣ − 4 ∣ + 6 = 4 + 6 = 10 y=|\sin x -5|+6=|1-5|+6=|-4|+6=4+6=\boxed{10}

Then, Sum of the max and min values = 12 + 10 = 22 =12+10 =\boxed{22}

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as we know range of sinx is b/w -1 t0 1..so 1 is maximum valve ..min of y=10 with sinx=1 and max of y=12 with sinx= -1 sum is=12+10=22

Faisal Yaseen - 7 years, 3 months ago

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