Trigono problem!
The sum of least and greatest possible value of 24 sin theta + cos theta
(Round the answer to integer)
The answer is 0.
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2 solutions
Note that 2 4 sin θ + cos θ = 2 4 2 + 1 2 sin ( θ + α ) , where tan α = 2 4 1 .
Hence, the maximum is 2 4 2 + 1 2 and the minimum is − 2 4 2 + 1 2 , and the sum is 0.
I have updated the answer to 0.
why can't sin theta be negative?
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the minimum value of a sin theta + b cos theta is -(a^2+b^2)^(1/2) and max (a^2 + b^2)^(1/2)
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No, that is not true. What happens when θ = − 2 π in your scenario?
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@Calvin Lin – Sorry i have changed the answer to 0 but the max and min values are as stated
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@Prince Loomba – I'm responding because you used the word "but", which sounds to me that you are disagreeing with what I said. If this is not the case, ignore this comment.
You were claiming that the minimum of 2 4 sin θ + cos θ is 2 4 2 − 1 2 . What is the value of the expression when θ = 0 ? Or when θ = 1 8 0 ∘ ?
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@Calvin Lin – Max value: (577^(1/2)) and Min value: -(577^(1/2))
For any equation a sin θ + b cos θ , the maximum and minimum values are a 2 + b 2 and − a 2 + b 2 which on addition gives 0 .