SAT 1000 problems - P1

Algebra Level 2

What is the minimum value of the function f ( x ) = 2 sin ⁡ x + sin ⁡ 2 x f(x)=2\sin x+\sin 2x for real x x ?

If the answer is A A , submit ⌊ − 1000 A ⌋ \lfloor -1000A \rfloor .


The answer is 2598.

Alice Smith by Alice Smith , 20, China

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1 solution

Minimum of f ( x ) f(x) is attained when cos ⁡ x = 1 2 \cos x=\dfrac{1}{2} , and sin ⁡ x = − √ 3 2 \sin x=\dfrac{-√3}{2} . The minimum value is − 3 √ 3 2 \dfrac{-3√3}{2} or − 2.598076... -2.598076...

0 Helpful 0 Interesting 0 Brilliant 1 Confused

How do you know that it must happen when cos ⁡ x = 1 2 \cos x = \frac12 and sin ⁡ x = − 3 2 \sin x = \frac{-\sqrt3}2 are fulfilled?

Pi Han Goh - 1 year, 10 months ago

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Using calculus.

A Former Brilliant Member - 1 year, 10 months ago

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