The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Trigonometric Identities Question

Does anyone know how to do this: 5sinx(sinx + cosx) = 3 for 0 < x < 360? I can’t seem to simplify it down in terms of sin x
(edited 2 years ago)
use the identity

sinxcosx=1/2(sin2x) 😊
Reply 2
Avatar for Emory
Emory
OP
6
Sorry, I forgot to put a + sign in between sinx and cosx.
(edited 2 years ago)
is the question asking to solve? Or simplify?
Reply 4
Avatar for Emory
Emory
OP
6
To solve
(edited 2 years ago)
image-a4cfeed3-0ed1-4a27-aaec-3a72fb210715204913652-compressed.jpg.jpeg
If it helps, these are all the possible trig identities you'll need at your level :smile: Let me know if you're still stuck
Reply 6
Avatar for mqb2766
mqb2766
21
Try dividing by cos^2 to get a quadratic in tan.
Reply 7
Avatar for OmariZ
OmariZ
5
Square both sides so that you can simplify the (sinx + cosx) to sin^2x + cos^2x = 1.

Pretty straight forward from there
Reply 8
Avatar for davros
davros
16
Original post by OmariZ
Square both sides so that you can simplify the (sinx + cosx) to sin^2x + cos^2x = 1.

Pretty straight forward from there

What will you do with the 2sinxcosx term?
Reply 9
Avatar for Emory
Emory
OP
6
Original post by davros
What will you do with the 2sinxcosx term?

I think you divide by cos x to get tan x
Reply 10
Avatar for Emory
Emory
OP
6
Original post by TaniaP
Does anyone know how to do this: 5sinx(sinx + cosx) = 3 for 0 < x < 360?I can’t seem to simplify it down in terms of sin x :/

8068A5CB-43A0-4EAE-8FD1-8133360A0B3B.jpeg I’ve solved it now thanks to everyone who help!
Original post by TaniaP
8068A5CB-43A0-4EAE-8FD1-8133360A0B3B.jpeg I’ve solved it now thanks to everyone who help!

I presume you realize that you could also factorize the sin & cos quadratic directly to get
(sin + 3cos)(2sin - cos) = 0
Solving it in terms of tan is arguably neater (especially if you use the quadratic formula) but nothing wrong with factorizing a quadratic like sin^2 + sin*cos + cos^2 directly.

Or if you divided through by cos^2 at the start, you can use the equivalent sec^2 <-> tan^2 identity to form the quadratic in tan.

Just for completeness, what you did is fine.
(edited 3 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you