# What is the range of trigonometric function y=-4*sin(51x+pi)?

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The range of a function is all the real values that f(x) can take for values of x that lie in the domain.

y = -4*sin(51x + pi)

Here x can take values in (-inf., inf.) but for any value of x, sin(51x + pi) can only lie in the interval [-1 , 1]

=> y = -4*sin(51x + pi) lies in the interval [-4 , 4]

**The range of y = -4*sin(51x + pi) is [ -4 , 4]**

The range of the sine function is known to be [-1 , 1].

Therefore, we'll put:

-1 =< sin (51x + pi) =< 1.

Now, we'll multiply the inequality by -4 and we'll change it's direction.

4 >= -4*sin (51x + pi) >= -4

We'll replace the expression -4*sin (51x + pi) by y:

-4 =< y =< 4

**The range of the given function is the closed interval [-4 , 4].**