Question

How do I figure out the successive tenths in this problem. It does not make any sense.
My homework: Sin (2 + 2pi)

use figure 6 (ill post a picture) to approximate the given trig values within successive tents. Then use a calculator to compute the values to the nearest hundreth.

Answer 1

there is an example in the book that doesnt make sense to me. ill place it here:
a) cos 3

answer: 3 is slightly less than pi, and pi radians is 180 degrees. so 3 radians is slightly less that 180 degrees. Thus in standard position the terminal side of an angle of 3 radians lies in the second quadrant. (HOW????) Therefore cos 3 is negative.

Answer 2

hmmm I do understand that cos(3) is negative....

now about the successive tenths.... maybe if you post a quick screenshot of the exercise itself? I mean, the picture you posted doesn't shed anything relevant to it, since all it's is a Unit Circle

Answer 3

okay @jdoe0001 and sorry i keep getting slow connection haha ill take a picture and send it right way

Answer 4

its example 6 in the book

Answer 5

hmm.... 6? is that the whole page on the left-side? because I think the top is a bit truncated

Answer 6

I dont know if its clear enought let me try another photo. But that is the example jus cos 3 sin 1 and tan 6. it just doesnt make sense

and my homework problem is :
\[\sin (2+ 2\pi)\] says to find the values within successive tenths. then use a calulator to figure the values to the nearest hundreth.

Answer 7

@jdoe0001

Answer 8

hmm... I see... do you know why cos(3) is negative?

Answer 9

3 = 3 radians that is, 1 radian \(\bf \approx 51^o\)

Answer 10

hmm 1 radian \(\bf \approx 57^o\) rather

Answer 11

@jdoe0001 this is what I see from the graph.
the circle is going around ever 10 units, lil squares.
Its 10 units up, down, left and right. but I dont ...........hmmm....is it that for every 10 around on the red line of the circle is a mark for 1 , 2 and 3. and when it says cos 3, I go to that mark that says 3. and the -x, +y so it makes it negative?

Answer 12

but.............how do i figure that on the calcualtor. okay I put my calculator in ...radian mode...hmmm then i put it like this right?
- cos (3) = but then i get .9899

Answer 13

and \(\bf cos(\theta) = \cfrac{adjacent}{hypotenuse}\implies \cfrac{a}{c}\implies \cfrac{x}{hypotenuse}\\ \quad \\
sin(\theta) = \cfrac{opposite}{hypotenuse}\implies \cfrac{b}{c}\implies \cfrac{y}{hypotenuse}\)

recall that "hypotenuse" is just the radius, and is neither negative nor positive, so the fraction, will be positive or negative depending on what the numerator is, and that will be "x" or "y" and that will depend on what Quadrant you're in

Answer 14

you're not expected to find the actual value for the trigonometric function, you're just expected to get the sign, is it positive or negative? just that, is all :)

Answer 15

ohhhhhhh...see that makes more sense, but then okay, my question is sin ( 2+ 2pi)

the 2 in the figure is in the 2nd quadrant so the sin would be positive,
but what about the + 2pi ?

Answer 16

does that just make the answer positive?

Answer 17

well... hmmm what's the sign of say \(\bf sin(2\pi) \quad ? \)

Answer 18

sin of 2 pi is 360 degrees @jdoe0001

Answer 19

@jdoe0001 did i get it right for the 2pi?

Answer 20

yes... well... 2pi is equivalent 360 .... but what's its sign of the \(\bf sin(2\pi)\)? negative or positive?

Answer 21

its positive, isnt it?

Answer 22

yes ok.... so.... now, we know that at 2pi, sine is positive, why? because \(\bf \cfrac{y}{hypotenuse}\) is positive because "y" is positive

Answer 23

2pi is on the 1,0

Answer 24

so now that we arrived at 2pi, let's go further, 2 more radians.... from 2pi, 2 radians further, what's sine? negative or positive?

Answer 25

YAY!!! that actually made more sense than the book did

Answer 26

oh man, hold on haha let me look at the circle

Answer 27

okay so the 2 pi means i go around the circle once, then i ad the 2 that takes me to the 2nd quadrant. cos is negative , leaving me with sin being positive right?! :D

Answer 28

@jdoe0001

Answer 29

\(\bf sin(2+2\pi)\qquad \cfrac{+y}{hypotenuse}\quad thus\quad \color{blue}{positive}\)

Answer 30

yeap

Answer 31

YAY!!! THANK YOU @jdoe0001 I get that now haha so cool, watch i forget by tomorrow. haha

Answer 32

hhehe yw