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# Rsin(x+a) help :) watch

1. Express 8 sin x+ 6cos x in the form Rsin(x+theta) where R>0 and 0<theta<90 degrees.

Dedude the number of roots for 0<x<180 degrees of the following equations.

a) 8sinx + 6cos x=5

Right so I worked out R to be = 10

So 10sin(x+theta)

Then 10sinxcos theta + 10sintheta cos x

10 sin x = 8

10 cos x = 6

Tan x = 8/6

So x = 53.1. How come theta is 39.1?

Like I can see if you add them up they make 90 but why specifically 90.

Also the bit in red how come we can't say 10costheta= 6 and then 10sin theta= 8 to work out theta by dividing them two? Thanks
2. (Original post by Super199)

10 sin x = 8

10 cos x = 6
these 2 lines are incorrect

8Sinx + 6Cosx = 10CostSinx + 10SintCosx (using t instead of theta)
3. (Original post by TenOfThem)
these 2 lines are incorrect

8Sinx + 6Cosx = 10CostSinx + 10SintCosx (using t instead of theta)
Would it be

10costheta=8
10sintheta=6

Tantheta=6/8
Then theta= 36.9

Say if I was looking to find x, is what I did initially correct? Or do you not work out x like that?
4. (Original post by Super199)
Would it be

10costheta=8
10sintheta=6

Tantheta=6/8
Then theta= 36.9

Say if I was looking to find x, is what I did initially correct? Or do you not work out x like that?
That is correct for theta

You are not trying to find x and you cannot do that anyway
5. (Original post by TenOfThem)
That is correct for theta

You are not trying to find x and you cannot do that anyway
Oh ok, thanks for the help
6. I need some more help if possible

Solve 7 sin x - 8 cos x=9 for all values between 0 and 2pi by

a) Expressing 7 sin x - 8 cos x in the form Rsin(x-a)
b). Using a graphical method

Right I think I have done part a and for my Rsin(x-a) bit I got

I think?

I then set that = 9 and did the normal stuff it's just part b I don't get

How do I solve it using a graphical method?
7. (Original post by Super199)
I need some more help if possible

Solve 7 sin x - 8 cos x=9 for all values between 0 and 2pi by

a) Expressing 7 sin x - 8 cos x in the form Rsin(x-a)
b). Using a graphical method

Right I think I have done part a and for my Rsin(x-a) bit I got

I think?

I then set that = 9 and did the normal stuff it's just part b I don't get

How do I solve it using a graphical method?
Use CAST to see if there are any more values of theta
8. (Original post by edothero)
Use CAST to see if there are any more values of theta
That's what I did but I didn't realise that counted as graphical.
9. (Original post by Super199)
That's what I did but I didn't realise that counted as graphical.
Some people (me included) skip using CAST and just do 180 - x // 180 + x // 360 - x without drawing it because its quicker. This questions ensures you use CAST and/or a different method, just for the sake of seeing some working out
10. (Original post by edothero)
Some people (me included) skip using CAST and just do 180 - x // 180 + x // 360 - x without drawing it because its quicker. This questions ensures you use CAST and/or a different method, just for the sake of seeing some working out
Oh lmao **** it cba, cheers anyway

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