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C2 Sequences and series question watch

1. (Don't have the symbol for theta so using x)
I'm having trouble with both parts of the question above.
For part a I have Sum = a / (1-r) = sin^2(x) / 1 - cos(x). I then substituted sin^2(x) with 1-cos^2(x) to get
Sum to infinity = 1-cos^2(x) / 1 - cos(x)
I have no idea how to rearrange this to get 1+ cos(x)?

For part b I used Sn = (a(1-r^n))/(1-r)
S6 = (sin^2(pi/3)(1-cos^6(pi/3))/(1-cos(pi/3)
And this gives 0.002003, but the answers say 1.48 (and 0.002003 seems incorrect if the sum to infinity is 1 + cos(x)). I can't work out what I've done wrong?
2. for part a You need to use sin^2 x=1-cos^2 x and then the difference of two squares in the numerator.

For part b You need to use Cos pi/3 = 1/2 and (possibly) Sin pi/3 = (root 3)/2 rather than go anywhere near your calculator. If you use the trick from a then you do not need the sin pi/3 value.
3. (Original post by nerak99)
for part a You need to use sin^2 x=1-cos^2 x and then the difference of two squares in the numerator.

For part b You need to use Cos pi/3 = 1/2 and (possibly) Sin pi/3 = (root 3)/2 rather than go anywhere near your calculator. If you use the trick from a then you do not need the sin pi/3 value.
Thanks! I've just realised that it's radians not degrees for part b, which explains why I've been getting the wrong answer. Difference of two squares seems so obvious now
4. (Original post by Lelanor)
Thanks! I've just realised that it's radians not degrees for part b, which explains why I've been getting the wrong answer. Difference of two squares seems so obvious now
What is this 'degrees' you speak of?

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