Can you please help me with this graphing question?
|
04-28-2014, 01:34 PM
Post: #1
|
|||
|
|||
Can you please help me with this graphing question?
Sec 4.6, #2. The question says "Graph two periods of the given tangent function"
y = 6 tan (x/6) And the the question goes on to say "Choose the correct graph of two periods of y = 6 tan (x/6) below" Answer choices: A) http://instagram.com/p/lRF07UEsHS/ B) http://instagram.com/p/lRF27UEsHV/ C) http://instagram.com/p/lRF6A-ksHW/ Please explain and show your work Ads |
|||
04-28-2014, 01:50 PM
Post: #2
|
|||
|
|||
The correct option is B)
Here is the steps Do you remember the curve y=tan x It is a periodic curve which passes through origin and as we go from -π/2 to π/2 the value of tan x increases So the curve goes on increasing from -π/2 to π/2 We also know,tan(-π/2)=not defined Actually, tan(-π/2)→ -∞ Also we know, tan(π/2)=not defined Actually, tan(π/2)→ +∞ Thus we have the curve y=tan x in the interval (-π/2,π/2) We know y=tan x is periodic with Period T=π So in order to get the curve y=tan x in the entire range of real numbers,just use it periodic property. That is, COPY and PASTE the curve in the domain (-π/2,π/2) to other intervals. ....................................................................................................................................................... Coming Back to our QUESTION In order to find the correct option,just use trial and error method Given, y=6tan(x/6) From this we can easily infer the following and using those inferences we can find the correct choice (1)Observe that y(0)=6tan(0/6)=0 Therefore the curve passes through origin (0,0) (2)When y=6, 6tan(x/6)=6 tan(x/6)=1 we know, tan(π/4)=1 Therefore, x/6=π/4 x=3π/2 Thus the curve must pass through (3π/2,6) (3)We know tan(-π/2) is -∞ For the curve y=6tan(x/6), x/6=-π/2 gives x=-3π Therefore y(-3π)=-∞ (4)We know tan(π/2) is +∞ For the curve y=6tan(x/6), x/6=π/2 gives x=+3π Therefore y(3π)=+∞ (5)Since y=tan x is an increasing curve,y=6tan(x/6) is also an increasing curve (6)The function Atan(Bx+C) is periodic with period π/B Thus y=6tan(x/6) is periodic with period 6π Using some or all of the above inferences we can see that B) is the correct choice. Ads |
|||
« Next Oldest | Next Newest »
|
User(s) browsing this thread: 1 Guest(s)