# More trig trauma!

• Feb 4th 2010, 06:22 PM
MathBlaster47
More trig trauma!
These questions get nothing but a blank stare from me....kinda irritating really since I sort of like trigonometry.

Describe each of the following graphs of y. Give (a) its amplitude (if applicable),(b) its maximum and minimum (if applicable) and (c) its period.
If it has no amplitude, maximum or minimum, write none in the appropriate space.

1
$\displaystyle y=3\sin\frac{1}{3}x$
(a) 3(I think)

(b)no idea

(c) $\displaystyle \frac{2\pi}{\frac{1}{3}}$ (I hope)

2
$\displaystyle y=\tan 2A$

(a) No clue

(b) Maximum:none and Minimum: none

(c) I wish I knew...

Thank you muchly once again!!
• Feb 4th 2010, 06:26 PM
pickslides
Here's a kick start for the period.

Period for $\displaystyle \sin(bx)$ is $\displaystyle \frac{2\pi}{b}$

Period for $\displaystyle \tan(bx)$ is $\displaystyle \frac{\pi}{b}$
• Feb 4th 2010, 06:33 PM
MathBlaster47
Quote:

Originally Posted by pickslides
Here's a kick start for the period.

Period for $\displaystyle \sin(bx)$ is $\displaystyle \frac{2\pi}{b}$

Period for $\displaystyle \tan(bx)$ is $\displaystyle \frac{\pi}{b}$

Ok....so the period for $\displaystyle y=3\sin\frac{1}{3}x$ is $\displaystyle \frac{2\pi}{\frac{1}{3}}$

and the period for [/COLOR][/COLOR]$\displaystyle y=\tan 2A$ is $\displaystyle \frac{\pi}{2}$?
• Feb 4th 2010, 07:56 PM
mattio
Quote:

Originally Posted by MathBlaster47
These questions get nothing but a blank stare from me....kinda irritating really since I sort of like trigonometry.

Describe each of the following graphs of y. Give (a) its amplitude (if applicable),(b) its maximum and minimum (if applicable) and (c) its period.
If it has no amplitude, maximum or minimum, write none in the appropriate space.

1
$\displaystyle y=3\sin\frac{1}{3}x$
(a) 3(I think)

(b)no idea

(c) $\displaystyle \frac{2\pi}{\frac{1}{3}}$ (I hope)

2
$\displaystyle y=\tan 2A$

(a) No clue

(b) Maximum:none and Minimum: none

(c) I wish I knew...

Thank you muchly once again!!

#1

A. amplitude is 3
B. since graph has no vertical shift and amp is 3, minimum is -3 & max is 3
c. period is 2pi/b, our b is 1/3 so period is 6pi

#2

A. amplitude is understood to be 1
B. thus, the minimum is -1 and the maximum is 1
C. period is pi/b, so pi/2
• Feb 7th 2010, 11:51 AM
pickslides
Quote:

Originally Posted by MathBlaster47
Ok....so the period for $\displaystyle y=3\sin\frac{1}{3}x$ is $\displaystyle \frac{2\pi}{\frac{1}{3}}$

and the period for [/color][/color]$\displaystyle y=\tan 2A$ is $\displaystyle \frac{\pi}{2}$?

Yep and yep.
• Feb 15th 2010, 02:37 PM
mathemagister
Hey MathBlaster47! Please keep in mind though, that the amplitude is the absolute value of the coefficient of the trigonometric term.

So if your first question was $\displaystyle y=-3\sin\frac{1}{3}x$, the amplitude would still be 3.

Just keep that in mind, that is a clever little trap that most tests use to catch students off guard. (I've seen this trap in every big trig test I took.)

Hope that helps you in your future endeavors (Wink)
• Feb 15th 2010, 04:46 PM
skeeter
Quote:

Originally Posted by mattio
#1

A. amplitude is 3
B. since graph has no vertical shift and amp is 3, minimum is -3 & max is 3
c. period is 2pi/b, our b is 1/3 so period is 6pi

#2

A. amplitude is understood to be 1 no
B. thus, the minimum is -1 and the maximum is 1 no
C. period is pi/b, so pi/2

the tangent function has no amplitude. it also has no maximum and minimum value since its range is $\displaystyle (-\infty , \infty)$
• Feb 16th 2010, 12:28 AM
mathemagister
That is also a good catch, Skeeter. So, to sum up what Skeeter and I have said about amplitudes.

The amplitude of $\displaystyle -3sinx$ is 3.

The amplitude of $\displaystyle 3cosx$ is 3.

The amplitude of $\displaystyle -3tanx$ does not exist.