Is amplitude always positive?

[nerd]

It’s me again! Still working through the review, but I can’t remember if the amplitude of a trigonometric function is always positive. Should my answer for 42c. be 2 or -2? Thank you!

(My teacher uses Comic Sans, I’m very sorry)

 

[Dr.Peterson]

It’s me again! Still working through the review, but I can’t remember if the amplitude of a trigonometric function is always positive. Should my answer for 42c. be 2 or -2? Thank you!
View attachment 33806

Yes, amplitude of a sinusoid is positive by definition. The negative sign results in a reflection.

Of course, when I do a search, among all the statements that amplitude is positive, I see videos of people graphing a sine with "negative amplitude", by which they probably mean the coefficient.

(My teacher uses Comic Sans, I’m very sorry)

You have my sympathy.

 

[nerd]

Thanks again

 

[Steven G]

If y= A*trig(x+B)+C, where trig can be replaced with sin, cos, tan,....
By definition, the amplitude = |A|, yes, the amplitude is never negative.