A geometry problem by Anik Mandal

Geometry Level 2

f ( x ) = sin ⁡ 2 x − 5 sin ⁡ x − 6 \large f(x) = \sin^2x-5 \sin x-6

If the range of the function above can be expressed as [ a , b ] a,b] , find a + b a+b .


The answer is -10.

Anik Mandal by Anik Mandal , 21, India

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1 solution

Tom Engelsman
Jun 21, 2017

Given that − 1 ≤ s i n ( x ) ≤ 1 -1 \le sin(x) \le 1 , we find that:

1 2 − 5 ( ( 1 ) − 6 = − 10 1^2 - 5((1) - 6 = -10 and ( − 1 ) 2 − 5 ( − 1 ) − 6 = 0 (-1)^2 - 5(-1) - 6 = 0

Thus, the range of f ( x ) f(x) is just [ − 10 , 0 ] [-10, 0] and a + b = − 10 + 0 = − 10 . a + b = -10 + 0 = \boxed{-10}.

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