Question

Can someone help me break down the following expression: x=3 sec (theta) reduces the expression square root of x squared - 9 enclosed in paranthesis to the following answers:
a. 3 sec (theta).
b. 9 sec squared (theta).
c. 9 tan squared (theta).
d. 3 tan (theta).

Answer 1

Am I in the right topic?

Answer 2

can anyone help me?

Answer 3

Howdy stranger ^.^
How can I be of service?

Answer 4

yes please

Answer 5

do you understand how I wrote the problem?

Answer 6

No. But for some reason, I think I already know the answer. Weird, huh? :D

Answer 7

want me to write out the problem more clearly?

Answer 8

Sure, why not?

Answer 9

\(\large \sqrt{x^2-9}\)

\(\large x = 3 \sec \theta\)

Answer 10

yes

Answer 11

simply substitute x value and simplify ?

Answer 12

wat does 3 sec theta mean though?

Answer 13

what ganeshie said.
it all boils down to that :D

Answer 14

but wait

Answer 15

wat does 3 sec theta equal?

Answer 16

x.
LOL

Answer 17

it equals x

Answer 18

\(\large \sqrt{ (3 \sec \theta )^2-9}\)

Answer 19

hmm

Answer 20

\[3\sec\theta= \frac3{\cos \theta }\]

Answer 21

give me a moment

Answer 22

3 sec theta minus 3?

Answer 23

\(\large \sqrt{ (3 \sec \theta )^2-9}\)

\(\large \sqrt{9 \sec^2 \theta -9}\)

\(\large \sqrt{9 (\sec^2 \theta -1)}\)

Answer 24

don't forget the "squared" part

Answer 25

so wait

Answer 26

ok

Answer 27

then?

Answer 28

then? 9 is a perfect square, so it comes out of the radical (its square root anyway)

Answer 29

so wait, would it be 3(sec theta+1)?

Answer 30

don't forget the squared on the sec...and the square root

Answer 31

hmm

Answer 32

you think you could write it out for me?

Answer 33

I'm still kinda confused at this part

Answer 34

lol of course ^.^
\[\Large \sqrt{9(\sec^2\theta \ - 1)}= \sqrt9\sqrt{\sec^2\theta \ - 1}= 3\sqrt{\sec^2\theta \ - 1}\]

Answer 35

ahh

Answer 36

so the 9 comes out of the radical and makes itself a radical

Answer 37

this is algebra stuff though :/

Answer 38

I'm sorry bro

Answer 39

I've never seen it done that way

Answer 40

well back to trigonometry...i'm sure you can find a suitable way to simplify \[\sec^2 \theta - 1\]right?

Answer 41

ahh yeah give me a moment

Answer 42

that equation sec squared theta-1=tan squared theta

Answer 43

so you're not totally lost after all :D
\[\Large 3\sqrt{\sec^2\theta \ - 1}=3\sqrt{\tan^2\theta}\]
Surely you can apply the finishing touch from here? ^.^

Answer 44

and that would simply to 3 tan (theta)

Answer 45

that does the trick, doesn't it? :)

Answer 46

yes

Answer 47

I appreciate it

Answer 48

do you think you could help me with another problem?

Answer 49

depends on the problem :D