Question

True or False The graph of y = cos x is decreasing on the interval $[0,\mathrm{\pi }]$.

Short answer

True Statement The graph of y = cos x is decreasing on the interval $[0,\mathrm{\pi }]$.

Step-by-step solution

Step 1. Given Information:

Given statement: The graph of y = cos x is decreasing on the interval $[0,\mathrm{\pi }]$.

We want to know that Is the given statement is True or False.

Step 2. Solution:

We know that

The cosine function is deceasing on the interval $[0,\mathrm{\pi }]$

We can also check the variation of the cosine function on the interval $[0,\mathrm{\pi }]$by interpreting the output of some values inside the given interval as follows:

$$\begin{gathered} \cos \left(0\right)=1 \\ \cos \frac{\mathrm{\pi }}{2}=0 \\ \cos \left(\mathrm{\pi }\right)=-1 \end{gathered}$$

Hence, we notice that the cosine function is decreasing on the interval $[0,\mathrm{\pi }]$.

Hence, the statement is True.