Question

Find the range of y= 3/2 cos 4x-1

Answer 1

Answer:

The range of y is $[-\dfrac{5}{2},\dfrac{1}{2}]$

Step-by-step explanation:

Given: $y=\dfrac{3}{2}\cos (4x) -1$

It is cosine function of trigonometry.

We need to find the range of given function. The value of y shows range of function.

y is depends on cosine function.

As we know cosine max/min value is fixed.

y is max when cosine max.

y is min when cosine is min.

Maximum value of cosine = 1

$y_{max}=\dfrac{3}{2}(1) -1=\dfrac{1}{2}$

Minimum value of cosine = -1

$y_{min}=\dfrac{3}{2}(-1) -1=-\dfrac{5}{2}$

Range of y: [min,max]

Range: $[-\dfrac{5}{2},\dfrac{1}{2}]$

Hence, The range of y is $[-\dfrac{5}{2},\dfrac{1}{2}]$

Answer 2

I have attached how to work through this problem. I hope this helps