Question

I need to find cos(2theta) if sin(theta)=1/5

Answer 1

Find theta by taking inverse sin of .2...then compute cos(2*theta)

Answer 2

how do I go about getting the inverse?

Answer 3

Calculator would be best bet...or maybe a lookup table. I'm sure google would do it for you

Answer 4

Yeah, I don't think they want them using calculators for this problem...

Answer 5

yeah it's a take home quiz and we can get help but we aren't supposed to use calculators

Answer 6

try this : \[\sin(\theta) = 1/5\]
so opposite =1 hypotenuse =5

Answer 7

adjacent = ?

Answer 8

\[\sqrt{25-1}\]

Answer 9

Ah yes good thinking

Answer 10

now look at your trig identities for \[\cos 2 \theta\]

Answer 11

one of them is going to be easy to use here... since you know
\[\cos \theta = (\sqrt{25-1} )/ 5\]

Answer 12

we haven't gone over identities yet. . .

Answer 13

you sure?

Answer 14

pretty sure, I am looking through my notes now. This is a retake quiz cause nobody aced it the first time and it's only three questions so I think the teacher may have forgotten to tell us something vital.

Answer 15

it's not just \[2\times(\sqrt{25-1})\] is it?

Answer 16

no

Answer 17

didn't think so. . .Could you teach me the identity?

Answer 18

trying to find another way of doing this geometrically, if you really aren't supposed to be using identities...

Answer 19

do you have a unit circle with (1/5, 1) as one of the angles? That's the easiest way...

Answer 20

hey I found some identity stuff on google,
Do I have to use \[1-2\sin^2(x)\]? and everything else that goes with it?

Answer 21

"one of the points for which an angle is given" is what I should've said.

Answer 22

Yeah, man you can use that, but if it's not what your teacher wants you to use... you might not get credit.

Answer 23

ok I will go for it. so do I just plug 1/5 in for x?

Answer 24

nope plug 1/5 in for sin(theta)

Answer 25

\[1-2(1/5)^2\]?

Answer 26

yes

Answer 27

Yeah, I was thinking of using an identity for cos(2*theta) that had cosine terms in it... but your way is easier... but are you sure you're allowed to use identities to solve this problem?

Answer 28

yeah I'm pretty sure, it says we will have to use a formula first as a hint on the problem

Answer 29

ok

Answer 30

So from that formula how do I get to \[\cos(2\theta)\]?

Answer 31

you already did
\[\cos 2\theta =1 -2\sin ^{2} \theta\]

Answer 32

so that's it? I can just have that as my answer?

Answer 33

calculate \[1-2(1/5)^{2}\]

Answer 34

what is it?

Answer 35

.92 or 23/25

Answer 36

that's it

Answer 37

My teacher said we don't have to fully simplify the answers and its a non calculator quiz. So that being said, is the unsimplified version the best answer to the problem?

Answer 38

23/25 then

Answer 39

ok sweet thanks for the help! Can I get your help on one more problem? or at can you least make sure I'm doing it right?