Question

What's the general form for the multiple angle....

cos x = -1/2
cos x = 0

Answer 1

Use the unit circle, so
so look for a value the x is -1/2, so 2pi/3, 4pi/3
look for value x is o, so pi/2,3pi/2
so final form use the period of cos 2pi
x= 2pi/3, 4pi/3+n2pi
x=pi/2+3pi/2+n2pi

Answer 2

Thank you. Do you mind helping with 1/2 more?

Answer 3

yes no problem, do you understand the problem?

Answer 4

whts the 2nd problem

Answer 5

I guess I'll tell you what I think and we'll see if I understand them.
It's x = 2pi/3 , 5pi/6, 5pi/3, and 11pi/6
The interval is [0,2pi)

Let me see what the general forms I think would be, one sec.

Answer 6

kk

Answer 7

Remember use unit circle and the trig functions period

Answer 8

Okay, no, I tried to follow what you said but I'm confused. Do you mind rephrasing it or something? :/ Sorry for the inconvenience, I usually pick these things up quickly.

Answer 9

Np, I am happy to help, I just finished studying, so I will make sure you understand it

The values you are given are radians from the unit circle, you need to find the values for sin and cos

cos is x coordinate and sin is y coordinate

so (x,y) is (cos,sin)
example 2pi/3, look on unit circle and coordinates are (-1/2,rad3/2) and sin and cosine period is at 2pi

1.) cos x= -1/2+n2pi, sin x= rad3/2 + n2pi

Let me know if you understand

Answer 10

Sorry I am a slow typer

Answer 11

No worries and I think I get it now but let's say there was an "interval", would that affect it in any way? I mean, would both of the general forms still be used or just one?

Answer 12

No the interval is telling you the period of cos and sin 2pi
all trig functions general period is 2pi, except for tan and cotangent which period is pi
when you need to worry about the intervals is when you start doing more trig identited sin(u+v)
so for this kind of problem you do not need to worry about it, just keep the general periods

Answer 13

So if my teacher were to ask for the general form of the angle, I'd have to put both of the general forms right?

Answer 14

I see here that it's:

5pi/6 = -sqrt3/2, 1/2
5pi/3 = 1/2, -sqrt3/2
11pi/6 = sqrt3/2, -1/2


As one example, would the 5pi/6 one be...
cos x = -sqrt3/2+n2pi, sin sin = rad1/2 + n2pi ?

Answer 15

yes exactly, good job!

Answer 16

In the first problem you have the find all values of (cos,sin), if given coordinates first

Answer 17

What do you mean?

Answer 18

in the first problem it gave us cos=-1/2 and cos=0
so in the unit circle we find when cosine is -1/2 and 0 for all the radian values
which was 2pi/3, 4pi/3 for -1/2, and pi/2, 3pi/2 for 0, and we put it in the general formula

In the seconf problem they gave us the radians such as 5pi/6 so we found the (cos,sin) (xy) coordinates (-rad3/2,1/2) and put it in the general form

Answer 19

So you would basically be doing the same thing or is there something different?

Answer 20

You would still plug the xy values in x=values+n2pi for both problems
1st problem it gave us cos=-1/2, cos=0
1.) use unit circle to find when cos is -1/2 and 0
2.) cos at -1/2, radian values 2pi/3, 4pi/3
3.) cos at 0, radian values pi/2, 3pi/2
4.) x= 2pi/3, 4pi/3 + n2pi for 1/2 coordinate
5.) x= pi/2, 3pi/2 + n2pi for 0 coordinate
6.) Remember cos is x coordinate (cos, sin) sin is y coordinate

2nd Problem we are given 2pi/3, 5pi/6, 5pi/3, 11pi/6
1.) It is saying when Cos radians is 2pi/3, 5pi/6, 5pi/3 11pi/6
and if we are finding Sin radians 2pi/3 5p/6, 5p/3 11pi/6
2.) Unit circle when Sin,Cos values at 2pi/3, 5pi/6, 5pi/3, 11pi/6
2pi/3 so Cos= -1/2, Sin=rad3/2, (-1/2, rad3/2)
5pi/6 so Cos= -rad3/2, Sin= 1/2 (-rad3/2,1/2)
5pi/3 so Cos= 1/2, Sin=-rad3/2 (1/2, -rad3/2)
11pi/6 so Cos= rad3/2, Sin= -1/2 (rad3/2, -1/2)
3.) Now plug in the values to the general form
Cos at 2pi/3, x= -1/2 + n2pi, Sin y=rad3/2 +n2pi
Cos at 5pi/6, x= -rad3/2 +n2pi, Sin y= 1/2 +n2pi
Cos at 5pi/3, x= 1/2 +n2pi, Sin y= -rad3/2 + n2pi
Cos at 11pi/6 x= rad3/2 +n2pi, Sin y= -1/2 + n2pi

Let me know if this makes sense

Answer 21

Perfect sense. Thank you.
I hate to feel like I'm bothering so if you'd like, just help me with this last one and that's it or I'll just keep looking online for help.

tan (3x) = 0
tan (x)-1 = 0

Answer 22

Np I will help you

Answer 23

kk 1 sec

Answer 24

you want the coordinates for this one also, right?

Answer 25

Just the forms if you'd like, since I can take the coordinate from them myself, right?

Answer 26

kk 1 sec, yes let me make sure

Answer 27

We are using the trig identites, right

Answer 28

kk got it

Answer 29

So tan(3x)=0, tan(x)-1=0
1.) tan(3x)=0
0/3 is 0
x= 0

2.) tan(x)-1= 0
tan(x)= 1
so sin/cos = tan
Values that get you 1 for tan
x= pi/4, 5pi/4
sin rad2/2/cos 2rad/2=1
sin -rad2/2/cos 2rad 2 = 1

Answer 30

Understand?

Answer 31

yes i believe so. where is says "rad" i wouldnt actually include that right?

Answer 32

i just wrrite the number? youve got your medal btw :)

Answer 33

thanks!, rad is square root sign, I would keep it in the work, I am working on your other problem, if you need anymore help, just notify me and I will finish your other problem

Answer 34

thanks a lot, love.

Answer 35

welcome!

Answer 36

kk i got it