question 9(multiple choice worth 1 points) (sine and cosine function graphs mc) the function j is defined as…

question 9(multiple choice worth 1 points) (sine and cosine function graphs mc) the function j is defined as j(θ) = cos θ. describe the behavior of the function on the interval from θ = π to θ = 3π/2. negative and concave up negative and concave down positive and concave up positive and concave down

question 9(multiple choice worth 1 points) (sine and cosine function graphs mc) the function j is defined as j(θ) = cos θ. describe the behavior of the function on the interval from θ = π to θ = 3π/2. negative and concave up negative and concave down positive and concave up positive and concave down

Answer

Explanation:

Step1: Analyze sign of cosine function

The cosine - function (y = \cos\theta) has the following property: when (\theta\in[\pi,\frac{3\pi}{2}]), (\cos\theta<0). We know that (\cos\pi=- 1) and (\cos\frac{3\pi}{2}=0), and the cosine function (y = \cos\theta) is continuous on the interval ([\pi,\frac{3\pi}{2}]).

Step2: Analyze concavity of cosine function

The second - derivative of (y = \cos\theta) is (y''=-\cos\theta). For (\theta\in[\pi,\frac{3\pi}{2}]), (y'' =-\cos\theta>0). When the second - derivative of a function (y = f(x)) is positive on an interval (I), the function is concave up on the interval (I).

Answer:

A. Negative and concave up