Question

help! will give medals- how do i start to solve this trig equation?
(tan θ − 2)(9 sin^2θ − 1) = 0

Answer 1

you can try
\(tan \theta -2 =0\) and \(9sin^2\theta -1 \)

Answer 2

\[(\tan \theta-2)(9\sin ^{2}\theta-1)\]

Answer 3

i thought about splitting them up, but then when i solve them, so i put both functions in my calculator? i got up to this point:

Answer 4

tanx=2 and sinx=1/3

Answer 5

sorry, i meant
\(9sin^2\theta -1\)=0

Answer 6

yes exactly

Answer 7

so do i plug them into my calculator now, or how d i go about using that info?

Answer 8

yeah, your calculator sould have a \(sin^{-1}\) function

Answer 9

yes, my text is saying there are 5 different answers though

Answer 10

sinx can be +1/3 or -1/3

Answer 11

thats where i got confused

Answer 12

ohh okay

Answer 13

well i can see three solutions lying within 0-360 degrees

Answer 14

it has something to do with the solution +pi k, then solution + 2pi K

Answer 15

\[\sin ^2\theta=\frac{ 1 }{ 9 },2 \sin ^2\theta=\frac{ 2 }{ 9 },1-\cos 2\theta=\frac{ 2 }{ 9 }\]
\[\cos 2\theta=1-\frac{ 2 }{ 9 }=\frac{ 7 }{ 9 }\]

Answer 16

are those double angle formulas?

Answer 17

yes

Answer 18

sorry didnt get what you meant by +pi k ....
between 0-360 there are ...many actually

Answer 19

i dont understand why i would need double angle formulas for it

Answer 20

here is the example problem:

Answer 21

\[\cos \alpha=\cos \left( 2n \pi \pm \alpha \right) \]

Answer 22

yea, i see it, the first solution is for tan, the next four are for sin, lying in each of the four quadrants

Answer 23

ohh okay, but how do i do the sin of 1/3?

Answer 24

or, rather, how would i go about getting those values?

Answer 25

use wolframalpha

Answer 26

huh?

Answer 27

for sin theta= 1/3 1st and 2nd quadrant,
theta and pi-theta
for sin theta =-1/3'
pi+theta and 2 pi- theta

Answer 28

http://www.wolframalpha.com/

Answer 29

were not allowed to use calculators, so i dont think i should use it

Answer 30

ohh

Answer 31

:( he makes us do everything manually

Answer 32

wow, this question will take quite a while then

Answer 33

actually, the answers are decimals, we must have to use a calculator. that wouldnt make sense. ugh. i hate trig.

Answer 34

and i just realized i have no clue how to find inverse manually xD

Answer 35

i dont even know. this crap is tough and he gave us 2 examples in class- which both were really basic. he throws stupid hard ones on the homework that have like, 5 solutions and shenanigans..

Answer 36

im just gonna email him

Answer 37

thank you for your help though!

Answer 38

sure :)