Use a graphing device to find the maximum and minimum values of the function $y = \cos x + \sin 2 x$

A)maximum value: $1.1$
, minimum value: $- 1.1$

B)maximum value: $- 1.1$
, minimum value: $- 0.76$

C)maximum value: $1.76$
, minimum value: $- 1.76$

D)maximum value: $2.76$
, minimum value: $- 2.76$

E)maximum value: $1.5$
, minimum value: $- 1$

Question

Use a graphing device to find the maximum and minimum values of the function $y = \cos x + \sin 2 x$

A)maximum value: $1.1$
, minimum value: $- 1.1$

B)maximum value: $- 1.1$
, minimum value: $- 0.76$

C)maximum value: $1.76$
, minimum value: $- 1.76$

D)maximum value: $2.76$
, minimum value: $- 2.76$

E)maximum value: $1.5$
, minimum value: $- 1$

Quizplus · Accepted Answer

The function $y = \cos x + \sin 2x$ combines a cosine wave and a sine wave. The maximum value of $\cos x$ is 1, and the maximum value of $\sin 2x$ is also 1, but due to the double angle, $\sin 2x$ can reach its maximum and minimum more frequently within the same period as $\cos x$. However, their peaks will not necessarily align perfectly due to their different frequencies and phases. The maximum theoretical sum occurs when both functions reach their peak simultaneously, which would give a value of 2, but due to the interaction of the waves, the actual maximum observed through graphing is slightly less, at approximately 1.76. Similarly, the minimum value is the sum of the minimum values of both functions, theoretically -2, but in practice, it's slightly less, at approximately -1.76, due to the same reasons.

Use a Graphing Device to Find the Maximum and Minimum y=cos⁡x+sin⁡2xy = \cos x + \sin 2 xy=cosx+sin2x

Use a Graphing Device to Find the Maximum and Minimum $y = \cos x + \sin 2 x$