Trigonometry is Impossible

Question

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10

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+1926

Umm, why is trig so hard. Take this problem as an example.

1. Find the maximum value of \(5cosA + 12sinA + 12\)

And good luck with this one...it's literally impossible. I don't even know where to start.

2. If tan θ + sec θ = l, prove that sec θ = (l^2 + 1)/2l

Thanks!

NotThatSmart Jun 18, 2024

CPhill · Answer 1 · 2024-06-18T03:54:07

1. 5cos A + 12sinA + 12 take the derivative and set to 0

-5sinA + 12 cos A = 0

12cos A = 5sinA

sinA / cos A = 12/5

tan A = 12/5

cos A = 5/13 sin A = 12/13

The max value is

5 (5/13) + 12 (12/13) + 12 = (25 + 144) / 13 + 12 = 169/13 + 12 = 13 + 12 = 25