Question

Find the exact value of sec(5pi/ 3) and and sin(7pi/6)

Answer 1

you know about coterminal angles?

Answer 2

yeah but im not sure how to find teh coterminal angles without converting it back to degrees. that is how my teacher likes it.

Answer 3

well, just realize that pi=180 degrees

Answer 4

ok

Answer 5

and then what to i do?

Answer 6

so sec x = 3/sqrt 2

Answer 7

wait isnt sec 1/cos 30 = 1/ (sqrt 3)/ 2

Answer 8

when i type it in teh calc it says 2 but i dont get taht when i work out teh problem

Answer 9

yes you mean sqrt(3)/2 because thats a 1,sqrt(3),2 triangle and yes it is 30 degrees

Answer 10

5pi/3 is 300 degrees

sec(300)
1/cos(300)
oh, then coterminal angle to 300 degrees is 60 degrees.

so we have 1/cos(60)
which is 1/1/2, which in turn is 2/1. Thus the value of sec(5pi/3) is 2

Answer 11

is your calculator in radians or degrees

Answer 12

you just got schooled kid

Answer 13

type in your calc. the cos^-1(sqrt(3)/2))=30 degrees

Answer 14

degrees

Answer 15

oh i read it wrong and yes i did get schooled BIG TIME

Answer 16

lol...its okay..thanks everyone for teh help...do u guys mind helping me w/ anotehr problem

Answer 17

now for sin(7pi/6)

7pi/6 is 210

Which means that we have sin(210), thus the coterminal angle is 30 degree, so in reality we have sin(30), this is a know value it is 1/2. Thus sin(7pi/6) is 1/2.

Thats right BIG TIME

Answer 18

i don't mind so long as you realize that there is no point in converting from degrees to radians!

Answer 19

or -1/2

Answer 20

i mean

Answer 21

trig has nothing to do with converting from some units to some other units. in fact this is a really bad idea because as functions trig functions are functions of numbers, not of angles

Answer 22

yeah i was trying to figure it out w/out converting degrees to radians.

Answer 23

i wasnt sure how though

Answer 24

there is no point in it whatsoever

Answer 25

if you see
\[f(x)=x^2\] you do not ask if x is in degrees or radians or Fahrenheit or Celsius or drachmas or pound sterling

Answer 26

x represents a number. and if you see
\[\sin(\frac{\pi}{2})\] it means the number
\[\frac{\pi}{2}\]

Answer 27

watch out the math police has come to arrest us for converting radians to degrees

Answer 28

damn right! your all busted.
find
\[\frac{7\pi}{6}\] on the unit circle on the last page of the cheat sheet. the second coordinate is sine

Answer 29

lol

Answer 30

@lagrange what is the derivative of sine? this is not a trick question

Answer 31

in your calculator if your in radians and your typing cos(30) will NOT be the same as cos(30) in degree MOde THATS what i am trying to see what he is in.

Answer 32

r u serious?

Answer 33

yes perfectly

Answer 34

cos (x)

Answer 35

simple point i am trying to make is that the derivative of sine is NOT cosine, not if you are viewing these as functions of "degrees"

Answer 36

that is as functions of numbers (not angles measured in whatever units you choose) trig functions correspond to the angle measure ONLY IN RADIANS

Answer 37

yeah im serious, go get a Calculator and put them in two different modes and type it. If you dont know what mode your in than youll get the wrong answer, do you see where im coming from. Ive seen it in my trig class 100 times

Answer 38

(just thought i would mention it)

Answer 39

taht is exactly what my teacher says except unforutnaltey in my head i am always converting it back and forth from radians to degrees.

Answer 40

so can u help me w/ anotehr problem? i wont convert it to degrees anymore.

Answer 41

i understand what you are saying from the get go, but he said when he was typing it in the calc he was getting something different. (Just thought i would mention that)

Answer 42

its find to convert radians to degrees and vice versa, just long as you dont get confused doing so

Answer 43

just know that eventually you will have to work with radians all the time, so get used to it

Answer 44

what the next problem??

Answer 45

word. didnt mean to come at you, sometimes i see these chats get all heated.

Answer 46

Find all teh values of x such that sin2x = sinx and
\[0\le x \le 2\pi\]

Answer 47

first of all subtract sinx from both sides:

sin2x-sinx=0

now use the trig identity: sin2x=2sinxcosx

2sinxcosx-sinx=0

factor out sinx
sinx(2cosx-1)=0

can you handle it from there?

Answer 48

you have to set each factor to zero

Answer 49

since sin(2x)=2sin(x)cos(x)=sin(x)
2cos(x)=1
cos(x)=1/2
since xE[0,2pi]
x=pi/3
x=pi+pi/3=4pi/3

Answer 50

do u find out what values of sin and cos equal 0?

Answer 51

sinx(2cosx-1)=0

sinx=0

2cosx-1=0

Answer 52

how do u find the other angles from 0 to 2pi

Answer 53

you have to find out at what values of x doe witthin that interval is sinx =0 and cosx=1/2

Answer 54

im not sure how.

Answer 55

and x=pi and x=2pi is also an answer. because in the top 2sin(x)cos(x)=sin(x)
doesnt matter what cos(x)= as long as the right side is the same
so as long as sin(x)=0 you also satisfy this equation
x=pi
x=2pi

Answer 56

at what values of x are sin=0 and cosx=1/2 within that interval

Answer 57

if it help the answers are: 0, pi/3,pi,5pi/3, and 2pi

Answer 58

when does sinx=0??


when does cosx=1/2??

Answer 59

i got the 0 and pi/3. how did u get teh other asnwers. @lagra...

Answer 60

look at the unit circle @ satellite provided you

Answer 61

i see it now. thanks

Answer 62

disreguard this pic wrong one, NOT 4PI/3 im sorry, but
sin(x)=0 at pi as well as 2pi

Answer 63

its 2pi-pi//3=6pi-pi/3=5pi/3