A trigonometric function is defined by y = A \cos(B x) + C, where A > 0 and B > 0. If the … — JAMB UTME

A trigonometric function is defined by $y = A \cos(B x) + C$ , where $A > 0$ and $B > 0$ . If the function has a maximum value of $7$ , a minimum value of $-3$ , and a period of $120^\circ$ , what is the value of $A + B + C$ ?

Answer: 10

Answer

The value of

A + B + C

is 10.

Solving the system

A + C = 7

and

-A + C = -3

gives

C = 2

and

A = 5

. Using the period relationship

120^\circ = 360^\circ / B

yields

B = 3

. Adding these parameters together gives

5 + 3 + 2 = 10

Step-by-Step Solution

Calculate vertical shift C and amplitude A

C = 2, A = 5

For y = A cos(Bx) + C, Max = A + C and Min = -A + C. Thus C = (Max + Min)/2 = 2 and A = (Max - Min)/2 = 5.

Calculate period coefficient B

B = 3

The period T in degrees is given by 360° / B. With T = 120°, B = 360° / 120° = 3.

Compute the sum A + B + C

Sum the derived parameters: 5 + 3 + 2 = 10.

Key Concept

Deriving amplitude, period coefficient, and vertical shift from trigonometric graph properties

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