Question

G is a trigonometric function of the form g(x)=acos(bx+c)+d

Below is the graph of g(x). The function has a maximum point at (3.5,-4) and a minimum point at (-1,-5)
Find a formula for g(x). Give an exact expression.

Answer 1

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Answer:

• a = 0.5
• b = π/4.5
• c = 7π/9
• d = -4.5

Explanation:

The value of d is the average of the maximum and the minimum.

d = (-4 +-5)/2 = -9/2 = -4.5

The value of 'a' is the difference between the maximum and d.

a = -4 -(-4.5) = 0.5

The value of b is 2π divided by the period. Here, the half-period is 3.5 -(-1) = 4.5, so ...

b = 2π/9 = π/4.5

The value of c is the value that makes the cosine argument zero at x=3.5.

(π/4.5)(3.5) +c = 0

c = -7π/9