# AS trig question

Hey all. Just wondering whether I could get some help for the following question:

6cos^2(theta) - 5 = 6sin^2(theta)+ sin(theta)

In the attached link is my workings: https://imgur.com/a/tiIusUz
Original post by Olly5847558
Hey all. Just wondering whether I could get some help for the following question:
6cos^2(theta) - 5 = 6sin^2(theta)+ sin(theta)
In the attached link is my workings: https://imgur.com/a/tiIusUz

sin can be -1/3 so why reject it?
Original post by mqb2766
sin can be -1/3 so why reject it?

Yes exactly but how can I have two answers? Do I just write down the angles for both values of x?
Original post by Olly5847558
Yes exactly but how can I have two answers? Do I just write down the angles for both values of x?

You can have 2 answers, that’s fine! Just means that multiple values satisfy the original equation.
Original post by Olly5847558
Yes exactly but how can I have two answers? Do I just write down the angles for both values of x?

Roughly speaking youve a quadratic in sin() so youd expect two solutions for sin() and each sin() will have two solutions on the domain 0...360 so youd expect 4 solutions.
https://www.desmos.com/calculator/qdwjv654wq

Obviously there can be less than 4 with the usual discriminant, trig values <-1 or >1 or = +/-1 ....
(edited 1 month ago)
Original post by mqb2766
Roughly speaking youve a quadratic in sin() so youd expect two solutions for sin() and each sin() will have two solutions on the domain 0...360 so youd expect 4 solutions.
https://www.desmos.com/calculator/qdwjv654wq
Obviously there can be less than 4 with the usual discriminant, trig values <-1 or >1 or = +/-1 ....

Makes sense, thank you so much