quick question on a trig graph

[brentwoodbc]

for the value of b I get 14/5 but the answer is 7/5

I do b = 2pi/period
period = 10pi/14 ****is that right I though it would be 7pi/10pi ie 7/10 but the answer has no pi so it has to have canceled/

so

2pi/(10/14) = 14pi/10 x 2pi
=14/5?

thank you

 

[wjm11]

for the value of b I get 14/5 but the answer is 7/5

I do b = 2pi/period
period = 10pi/14 ****is that right

Not quite right. Notice that on your graph, there are seven squares/units from zero to pi. There are 10 squares/units for the period of the sinusoidal function. Therefore, the period is (10/7)pi or 10pi/7.

b = 2pi/(10pi/7) = 7/5.

Hope that helps.

 

[brentwoodbc]

but the period of a sinusoidal function is 2pi, so why do you go from 0-pi?

 

[mmm4444bot]

… why do you go from 0-pi?

This was done to determine how wide each square is on the graph.

The period of the function graphed is obviously 10 squares wide.

We can't divide 2 Pi by the phrase "ten squares" ! :wink:

We need to express the period as a Real number.

Since there are seven squares from 0 to Pi, each square must be 1/7th Pi units wide.

So, the distance of ten squares must add up to 10 * 1/7th Pi.

So, the period is (10/7) Pi -- a Real number!

So, we divide 2 Pi by (10/7) Pi, as shown in the previous explanation, to determine the value of b.

 

[brentwoodbc]

thank you.