Need help!! 8. Solve for theta. 0

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Need help!! 8. Solve for theta. 0

Mathematics
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factor out cos \[\cos(\theta)(5\sin(\theta) -3) \] now set each factor to zero and solve \[\cos(tehta) = 0~~~and~~~5\sin(\theta) - 3 = 0\]
|dw:1434604876572:dw|
can someone plz help me

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From your unit circle you can pick out where cosine is 0. For the sine solutions, you already have sin Θ = 0.6. Use the sin^-1 button on your calculator to find Θ Θ = sin^-1 (0.6) This gives an angle in the 1st quadrant. sine is also positive in the 2nd quadrant. Subtract the other solution from pi to get the angle in the 2nd quadrant. Θ = π - sin^-1 (0.6)
do still need help i would have messaged u but i got blocked for god knows what
Θ = sin^-1 (0.6) i get 37 degree
ican help or fleather me
@SkaterBoyShawn what is ur problem
I don't need ur help
i have no prob u said fleather me then blocked me i am confuesd make sense i dont know what i did to u
inb4 crazy ban from original poster ...stop mass tagging people.
yes 37° is one solution. 180° - 37° = 143° is another solution
now what did i do
wait but at the back the answer is different
it is something like 74
stop tagging me iam bothing u so leave me alone bye have a good evning
we can factor out cos( \theta), so we can write: \[\Large \cos \theta \left( {5\sin \theta - 3} \right) = 0\]
you have missed on of the key aspects of the question, you are working in radians and you should have 4 angles as the solution
no@campbell
the answer is given in degrees
@MTALHAHASSAN2 yes he's right. It is in radians
you solutions to the factor are correct.. \[\cos(\theta) = 0\] what 2 angles measure make this true, remember its in radians...
"0
oh yeah
my bad
the domain is given as \[0 < \theta l< 2\pi\] so you should answer in radians
yep the answer is in radian
so the solutions for \[\cos(\theta) = 0\] should be straight forward the 2 angles for \[\sin(\theta) = \frac{3}{5}\] are in the 1st quadrant and 2nd quadrant
5sin(θ)cos(θ)-3cos(θ) = 0 divide by 5 sin(θ)cos(θ) -3/5cos(θ)=0 3/5=sin37(approx) sin(θ)cos(θ)-sin(37)cos(θ)=0 cos(θ)[sin(θ)-sin(37)]=0 either cos(θ)=0 i.e, (θ)=90 or sin(θ)-sin(37)=0 i.e (θ)=37 or 143 :)
does that make sense..?
so 37 and 143 be the answer
but i have to convert that in radians
so find the 1st quadrant angle for theta and then 2nd quadrant is \[\pi - \theta\]
this online calculator will do it for you http://web2.0calc.com/ just select radians
then input the ratio
how
select radian press 2nd... then asin which is arcsin \[asin = \sin^{-1}\] then enter 0.6 and = what do you get?
oops should select Rad.. bottom left corner
ok
then 2nd asin (0.6) =
0.605
the solutions are 90 = pi/2 rad 37=37pi/180 rad 143=143pi/180 rad do the calculations and get the answer in radians
ummm not quite... I got 0.6435011.... can you just check again you have to press 2nd to before closing the brackets then =
i goted 0.64
great so that is the 1st quadrant answer to the nearest hundredth now the 2nd quadrant is \[\pi - 0.64\]
2.50
right
yes.. that's it... well done
wait but at the back they have four solution
these two are the same but we are missing two
ok... so they are the values for sin now the values of cos you have \[\cos(\theta) = 0\] what angles make it true..?
90
here is the curve |dw:1434608602050:dw|
remember its in radians
pie/2
so where does the cos curve cut the horizontal axis..?
great, that's 1 and the other is..?
270 which is 3pie/2
that's correct... so you have 4 angles...
yes thanks a lot
glad to help

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