Question

Predict the Maximum value, the Minimum value, and the values of x where they occur for each function on the interval x E [-2pi, 2pi]

A) y = sinx + 4
B) y = cosx =5
C) y = sinx -2
D) y= cosx +1

Answer 1

largest value of sine is 1 so largest value of \(\sin(x)+4\) is \(1+4=5\)
others are similar

Answer 2

Hey, so sinx +4 is the sin wave just shifted up 4. sin has a range of (-1,1) and if you shift the center of sin up 4 the new range is from (3,5). the rest are similar.

Answer 3

On the Answer sheet it says Maxima (-3pi/2, 5) , (pi/2, 5)...Minima (-pi/2,3), (3pi/2, 3)

How do they get those numbers with the pi's?

Answer 4

Okay to sin has a cycle of 2pi. if you divide 2pi into 4 qudrants youll get all the x values for the mins and max. so, pi/2 is first , second pi, third 3pi/2 and fouth is 2pi.

Answer 5

pi/2 +pi/2 + pi/2 + pi/2 = 2pi one full cycle.

Answer 6

alright

Answer 7

makes sense...90 90 90 90 = 360

Answer 8

but how do they get -3pi/2?

Answer 9

wheres the -3?

Answer 10

Oh, your interval is from [-2pi, 2pi] so do the same thing going going to the negative x (or left side of yaxis.

Answer 11

but its a translation up 5, why is it -3pi/2

Answer 12

I understand how to get my y values for (x, y) but I am clueless for my x values anyone help??

Answer 13

@rob1525 I still don't get it on how to get the x :S please help!

Answer 14

when you translate it up 5 your not shifting the grap left or right so the period is still between 0 and 2pi. you can also going the negative direction and still have the same period just neg. so -pi/2 , -pi... but if you graph it you see the y values are reverse to the positive side.

Answer 15

but its -3pi/2 not just -pi/2