Trigonometry at its best........................

Geometry Level 2

Find the maximum value of 3sinx + 4cosx + 7.


The answer is 12.

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Srutarshi Chakrabarti by Srutarshi Chakrabarti , 23, India

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2 solutions

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Gagan Raj
Feb 15, 2015

For this equation , maximum occurs at x = 45 degrees.

Maximum Value = 3 sin(45) + 4 cos(45) + 7

= ( 3 + 4 ) / root(2) + 7

= 7 / root(2) + 7

= approx. value is 5 + 7

= 5 + 7 = 12

Thus maximum value of this equation is 12.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

What's the justification behind your telling that it is max. at 45 degrees?

Srutarshi Chakrabarti - 6 years, 3 months ago

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Hello Srutarshi!!! Your questioning for my solution is a very good one. Here is the justification you wanted.

We all are aware of the function y = sin x + cos x

This problem is similar to this function.

Differentiating both the sides with respect to ' x ' we get ,

y' = cos x - sin x

Equating the derivative to zero we get ,

cos x - sin x = 0

cos x = sin x

This condition holds good only when x = 45 degrees.

Hence the maximum of the given function occurs at x = 45 degrees and hence my solution.

If you have any objections please feel free to reply back and if i have done any mistake please feel free to correct me. Thank You!!!

Gagan Raj - 6 years, 3 months ago

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Nice solution my friend but Gagan what about the younger ones who don't know derivatives?? Let me give another solution. That way there won't be any doubts.

Srutarshi Chakrabarti - 6 years, 3 months ago

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