# Triganometrical Identities help :/Watch

#1
Solve for ?, in the intervall 0<?<360 for the equation 4sin?=tan?

somthing to do with tan?=sin?/cos? i'm guessing but... I keep going wrong :/

Any help would be much appreciated

(? being theta... TSR doesn't like unicode it seems)
0
7 years ago
#2
Use that identity, remove the sines and then you have something in cos which is then possible to solve.

Failing that.
What you do is 0<n<360 then 1tan?=4sin.
Then take away 3 plus the 2 minus the 7 times by 69.
Then leave it to bake for 5 minutes.
2
7 years ago
#3
Use that identity, cancel the sines and then you have something in terms of cos which you can solve.
0
7 years ago
#4
(Original post by J.tytler)
Solve for ?, in the intervall 0<?<360 for the equation 4sin?=tan?

somthing to do with tan?=sin?/cos? i'm guessing but... I keep going wrong :/

Any help would be much appreciated

(? being theta... TSR doesn't like unicode it seems)
Rewrite the tan theta as sin theta/cos theta. Multiply through by cos theta, subtract sin theta, factorize and solve for theta.
0
7 years ago
#5
(Original post by ben-smith)
Use that identity, cancel the sines and then you have something in terms of cos which you can solve.
You don't cancel the sines as you lose solutions associtated with sin theta=0.
0
7 years ago
#6
(Original post by J.tytler)
Solve for ?, in the intervall 0<?<360 for the equation 4sin?=tan?

somthing to do with tan?=sin?/cos? i'm guessing but... I keep going wrong :/

Any help would be much appreciated

(? being theta... TSR doesn't like unicode it seems)
let theta = x

4sinx = tanx
tanx = sinx / cosx

4sinx = sinx / cosx

4sinx cosx = sinx

4sinx cosx - sinx = 0

sinx (4cosx - 1 ) = 0

sinx = 0 x = 180 ( not 0 or 360 since it must be <360 and >0 )

cosx = 1/4

Do cos^-1 (1/4) on your calculator to get the principle angle, then use the CAST method or (360 - angle) to get the second value .

It all comes down to manipulating algebra and rearranging this and that...
0
7 years ago
#7
(Original post by Gemini92)
You don't cancel the sines as you lose solutions associtated with sin theta=0.
I'm starting him/her off, not doing their homework. Those solutions should have been noted a priori as they can be done by inspection.
0
#8
(Original post by sohail.s)

sinx = 0 x = 180 ( not 0 or 360 since it must be <360 and >0 )

cosx = 1/4
Thanks, I didn't even realize it had solutions for 0, 180 or 360 as I had simply, and erroneously divided by sinx ignoring the fact that sinx=0

Good job you pointed that out
0
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