Find maximum and minimum values of a trigonometry function

Question:

Find the maximum and minimum values of a trigonometry function y = 4 cos²x + 1

Solution:

using the formula: cos²x = (cos 2x + 1)/2

y = 4 cos²x + 1

= 4 (cos 2x + 1)/2 + 1

= 2 (cos 2x + 1) + 1

= 2 cos 2x + 2 + 1

= 2 cos 2x + 3

Because the range of cos 2x is: -1 <= cos 2x <= 1

when cos 2x = -1, y = 2 × -1 + 3 = -2 + 3 = 1.

when cos 2x = 1, y = 2 × 1 + 3 = 2 + 3 = 5.

Therefore, the maximum value of the function y is 5 and the minimum value of the function y is 1.

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