Sketch the graph of each function in the interval from 0 to 2pi

Question

omarbirjas · Answer

$$y=2\cos(\frac{ \pi }{ 2})\theta$$

campbell_st · Answer

what do you know about the curve?   amplitude and period..?

omarbirjas · Answer

how many cycles it makes from 0 to 2pi

campbell_st · Answer

ok...a standard form is 

$$y = a \cos (bx) $$

a = amplitude... so in your question a = 2

the value of b in your question is 

$$b = \frac{\pi}{2}$$

and the period is found by 

$$period = \frac{2\pi}{b}$$

to to find the period in your curve its 

$$period = \frac{\pi}{\frac{\pi}{2}}$$

so can you simplify it..?

omarbirjas · Answer

1/2

campbell_st · Answer

oops... the period is 

$$period = \frac{2\pi}{\frac{\pi}{2}}$$

sorry for the mistake

omarbirjas · Answer

1

omarbirjas · Answer

no probs

campbell_st · Answer

well you are dividing by a fraction so flip and multiply 

$$2\pi \times \frac{2}{\pi} = 4$$

so over a distance of 4, the curve completes 1 cycle

omarbirjas · Answer

what? how does it equal 4?

campbell_st · Answer

the period 

$$period = \frac{2\pi}{\frac{\pi}{2}} $$

I think you'll find that the period is 4 if you simplify it.

omarbirjas · Answer

Well i put it in a calc and got 1

campbell_st · Answer

if you would like to check you can use https://www.desmos.com/calculator it's an excellent online graphing site

omarbirjas · Answer

i tried it....it gave me a straight line...

omarbirjas · Answer

http://www.wolframalpha.com/input/?i=%282pi%29%2Fpi%2F2

campbell_st · Answer

replace theta with x... and you will get the curve

campbell_st · Answer

and if you feel the period is 1... then that's what you should use.

omarbirjas · Answer

i just want to know how its 4

campbell_st · Answer

$$\frac{2\pi}{\frac{\pi}{2}} = 2\pi \div(\pi \div 2) = 4 $$

the rule for dividing by a fraction

1. find the reciprocal of the fraction. 

2. multiply

campbell_st · Answer

so 

1. reciprocal is 

$$\frac{2}{\pi}$$

2. multiply

$$2\pi \times \frac{2}{\pi} = 4$$

omarbirjas · Answer

why do we reciprocate?

campbell_st · Answer

that's the rule for dividing by fractions... 

the question is asking 

$$how~~many~~~\frac{\pi}{2}~~~ make ~~2\pi$$

and you need 4

omarbirjas · Answer

ohhh ok

omarbirjas · Answer

gotcha...proceed please

campbell_st · Answer

so now you know the period and amplitude you can draw the graph. 

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its a rough sketch... but I hope it makes sense