maths C2 trig help!

Hi, I'm stuck on a few trig eq. Q out the textbook;

Solve the equation 3sin^2x=1+5cosx in the range 0-180

Solve the equation cos(3x-pi)=-1

I understand everything else I just need help in rearranging the equations (possibly using the identities) to find x! I can't quite get it right, help would be appreciated, ty.
-A

Original post by anton6846

Hi, I'm stuck on a few trig eq. Q out the textbook;

Solve the equation 3sin^2x=1+5cosx in the range 0-180

Solve the equation cos(3x-pi)=-1

I understand everything else I just need help in rearranging the equations (possibly using the identities) to find x! I can't quite get it right, help would be appreciated, ty.
-A

If you want help rearranging, just post your attempt at the rearrangement and we'll tell you exactly where the errors lie.

Reply 2

Dysf(x)al

20

Original post by anton6846

Hi, I'm stuck on a few trig eq. Q out the textbook;

Solve the equation 3sin^2x=1+5cosx in the range 0-180

Solve the equation cos(3x-pi)=-1

I understand everything else I just need help in rearranging the equations (possibly using the identities) to find x! I can't quite get it right, help would be appreciated, ty.
-A

For the first one, have you tried expressing sin²x in terms of cosx? Think about identities.

Reply 3

anton6846

OP

1

Original post by RDKGames

If you want help rearranging, just post your attempt at the rearrangement and we'll tell you exactly where the errors lie.

Well I've moved pi to the RHS and divided by 3 but I know this is wrong?

Original post by TheMindGarage

For the first one, have you tried expressing sin²x in terms of cosx? Think about identities.

o ya thanks ill give it a go.

Original post by anton6846

Well I've moved pi to the RHS and divided by 3 but I know this is wrong?

Seems like a valid portion of the full procedure. Must be going wrong elsewhere if you can't get the correct answer.

Reply 5

the bear

20

you must learn these:

https://mathsteaching.wordpress.com/2008/04/29/c2-trigonometric-identities/

Reply 6

NatalieDouglas

Original post by anton6846

Hi, I'm stuck on a few trig eq. Q out the textbook;

Solve the equation 3sin^2x=1+5cosx in the range 0-180

Solve the equation cos(3x-pi)=-1

I understand everything else I just need help in rearranging the equations (possibly using the identities) to find x! I can't quite get it right, help would be appreciated, ty.
-A

The first one needs to be converted into a quadratic in cos(x) first. You can inverse cos both sides of the second but you will need to extend the interval to get all solutions. There are two examples just like this at this link:
http://studywell.com/maths/pure-maths/trigonometry/trigonometric-equations/
Hope that helps.

maths C2 trig help!

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