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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