Question

Find the exact value of the following expression. If undefined, state, undefined. sec((cot^(-1)(5/12))
can some one pls write this down step by step: I ma going nuts trying to use the the identity
sec2x=1+tan2x

Answer 1

do I first change cot to tan? then square it?

Answer 2

Akileez i explained this earlier on - check it out.

Answer 3

thanks uzma; I knwo you replied previously to it

Answer 4

I know jimmyrep; I wen tover it again and was confused

Answer 5

cot^-1(5/12)=x
5/12=cotx
tanx=12/5

Answer 6

I did< i understand from using a right angles triangle. but i want to understand from a substitution perspective too.

Answer 7

now use the identity

Answer 8

oh ok yes change cot to tan tan = 1/cot then square it and plug it into the formula

Answer 9

ok got that, but what about the sec in front after using the identity?

Answer 10

take the sqrt

Answer 11

and how/why can you put an equals sign from tan(12/5) to tanx=12/5

Answer 12

is it by adding the x component?

Answer 13

\[secx=\sqrt{1+(12/5)^2}\]

Answer 14

cotx=5/12
i/tanx=5/12
tanx=12/5

Answer 15

cot is the reciprocal of tan

Answer 16

yes, got that

Answer 17

this is what i get:

Answer 18

sec(sec^2x=25/144)

Answer 19

sec(sec^2x=(25/144) + 1)

Answer 20

how come?

Answer 21

just solve what i posted earlier

Answer 22

I'll show you what I did: sec(tan(5/12))

Answer 23

now I originally changed tan to sin over cos and changed sec to I/cos - but that left me with sin

Answer 24

my issue is that I do not see how you manage to cancel the trig funtions out and come up with just a number

Answer 25

I really appreciate your help as this is bothering me as it shld be so obvious,

Answer 26

u r not need to change it, we have got the value of tanx, plug it into the identity n do the computations

Answer 27

its ok, just be clear at ur end :)

Answer 28

will do:

Answer 29

can we start with the cot^-1 part first ?

Answer 30

ok

Answer 31

u post what u think

Answer 32

that would change to tan

Answer 33

therefore you now have sec(tan(5/12)) - is that true>?

Answer 34

no its not right

Answer 35

ok, this is where I am stumped - sorry.

Answer 36

let
cot^-1(5/12)=x
5/12=cotx
tanx=12/5

Answer 37

ok?

Answer 38

remind that what is x taken to be

Answer 39

ok, got that - forgot the ^(-1)

Answer 40

therefore it shld now read sec(tan(12/5))

Answer 41

is that correct?

Answer 42

now dealing with the tan part first: now, tan^2x+(12/5)^2 is that right?

Answer 43

no

Answer 44

ok, so what goes after sec(tan(12/5)) ?

Answer 45

or are you first dealing with tanx=12/5?

Answer 46

how did u get it?

Answer 47

yes after getting tanx=12/5
use the identity

Answer 48

sec x

Answer 49

ok great: then after squaring: I will have sec^2x-1=144/25

Answer 50

= (144/25) - 1

Answer 51

sec^2x=1+144/25

Answer 52

i have an idea. draw a 5 - 12 - 13 right triangle. cotangent is "adjacent over opposite" so label the angle accordingly. that is label the angle whose opposite adjacent side is 5 and whose opposite side is 12. then all the other trig functions of that angle should be obvious

Answer 53

( sorry plus one) then I will have to solve: sec(1 +144/25)

Answer 54

yes sat.. u r right, but he/she wanted to do with identity :)

Answer 55

sec x=13/5

Answer 56

thanks anyway Sat

Answer 57

so you dont solve it further?

Answer 58

it is done , y further?

Answer 59

what I mean is:

Answer 60

ok do it the hard way, fine with me!

Answer 61

:)

Answer 62

you have sec(169/25) right?

Answer 63

haha; sorry, hard way it is

Answer 64

no no,

Answer 65

actually it became hardest :P

Answer 66

from sec(144/25+1)

Answer 67

all the identities come right out of the triangle anyway. i will be quiet now

Answer 68

haha; i am sooooo sorry: that i am such a pain, just really want to get it

Answer 69

now satellite is here, he is so sweet, would make u understand

Answer 70

its ok, no pain, no gain :)

Answer 71

up to this part: sec^2x=1+144/25

Answer 72

right

Answer 73

take squre root

Answer 74

oh first simplify the right side

Answer 75

ok, that leaves us with sec 13/5

Answer 76

sorry; first simplify

Answer 77

u missed x again

Answer 78

169/25

Answer 79

sec^2x =169/25

Answer 80

so sec^2(x) = 169/25

Answer 81

sec x=13/5

Answer 82

therefore sec =13/5

Answer 83

my issue i show we did away with the sec outside the (cot^(-1)(5/12)) - am I being clear?

Answer 84

yup :)

Answer 85

when u get secx =13/5
put the value of x back
sec(cot^(-1)(5/12)=13/5

Answer 86

oh now I see!!!

Answer 87

yay!!! i am so happy! thank you millions and millions!

Answer 88

my pleasure, if i made u understand, i m done

Answer 89

practically it all came dow to saying let cot^(-1)(5/12) = x

Answer 90

you rock!!!

Answer 91

hahaha, i asked u keep it in mind

Answer 92

I was so busy trying to cross out the trig functions, that's why I missed it all the time

Answer 93

thank you so much for your help!

Answer 94

take care:)