Thread: trigonometric equations

I can't seem to do (a)(ii) of this question, there are probably two ways to do it but i get stuck using my way.
Given find the value of E and the value of where R>0 and 0<
[I got R = 5 and [tex]\alpha=0.6435 rads which is right]

Hence ind all values between 0 and 2 satisfying
(a)(i) 4cos
[i also got this right its 1.8 and 5.77 rads]
(ii) 4cos
i expanded again and got 5cos( but i dont know where to go from here,,,ive come across a similar scenario before and cant remember what I did, If anybody could help that'd be great, thnx

If two angles α and β (between 0 and 2π) have the same cosine then either α = β or α + β = 2π.

hmm but the answer givwen is 0.21,0.64,2.31 and 4.4 rads how did u get at least two of them exactly,,,do you use sina +sinb=2sin(a+b/2)cos(a+b/2) or is that possible?'', oh i see what you mean now but that only gives me 0.6435 ans 0.231

You know that . Cancel the 5s, then you see that you have two angles with the same cosine. there are then four possibilities:

1. .

2. .

3. .

4. .

You could add any multiple of 2π to the right-hand side of 1. or 2., but the only ways to get solutions for θ in the interval from 0 to 2π are the four given above.

thanks!! I get the right answer now, Is that some rule to remember i.e for the limit of 2 you can only go to twice i.e 4pi or is there some kinda proof i could search in the internet thanks!?