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# Trig question watch

1. a) tan(3x+20degrees)=3/2

b) 2sin^2x+cos^2x=10/9

I'm unsure on how to work these out. Any help would be appreciated.
2. (Original post by dippers)

a) tan(3x+20degrees)=3/2

b) 2sin^2x+cos^2x=10/9

I'm unsure on how to work these out. Any help would be appreciated.
For part a), take arctan of both sides, and then solve for x:

For part (b) you need to use the R formula:

Also, what's the range for the answer meant to be (0 to 180, -180 to 180, 0 to 360...)?
3. (Original post by Qwertish)
For part a), take arctan of both sides, and then solve for x:

For part (b) you need to use the R formula:

Also, what's the range for the answer meant to be (0 to 180, -180 to 180, 0 to 360...)?
Sorry, the range is -90<x<90

I've figured out how to do the first one I got 12.1 and -25.4
and i'm unsure on how to do the second one I know i input 1-sin^2(theta) for cos^2(theta) but then i don't know what to do.
4. (Original post by dippers)
Sorry, the range is -90<x<90

I've figured out how to do the first one I got 12.1 and -25.4
and i'm unsure on how to do the second one I know i input 1-sin^2(theta) for cos^2(theta) but then i don't know what to do.
Oh, sorry, those are sin^2... It's just this:

5. (Original post by Qwertish)
Oh, sorry, those are sin^2... It's just this:

was just about to type this
6. (Original post by Qwertish)
Oh, sorry, those are sin^2... It's just this:

Thank you so much! It seems simple when I look at it now! And did I get the first one right or were there more solutions?
7. (Original post by dippers)
Thank you so much! It seems simple when I look at it now! And did I get the first one right or were there more solutions?
I think there should be 3 solutions (for tan, there is a solution every 180 degrees, and your adjusted range will span 540 degrees).

I'll check it now (if TenOfThem doesn't beat me to it )

EDIT:
Yep, there should be three. One negative and two positive.
8. (Original post by Qwertish)
(if TenOfThem doesn't beat me to it )
The rugby is slowing me down
9. (Original post by Qwertish)
I think there should be 3 solutions (for tan, there is a solution every 180 degrees, and your adjusted range will span 540 degrees).

I'll check it now (if TenOfThem doesn't beat me to it )

EDIT:
Yep, there should be three. One negative and two positive.
Oh yeah I know now, thanks guys!

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