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Find the solutions of the equation 3cos(2 theta) - 5cos(theta) + 2 = 0 in the interval 0 < theta < 2pi.

3cos^2(theta) - 3sin^2(theta) - 5cos(theta) + 2 = 0 3cos^2(theta) + 3cos^2(theta) - 3 - 5cos(theta) + 2 = 0 6cos^2(theta) - 5cos(theta) - 1 = 0 delta = 25 + 24 = 49 cos(theta) = (5 - 7)/12 = -1/6 or cos(thet...
PW
Answered by Piotr W. • Maths tutor
5804 Views

I'm trying to integrate f(x)=sin(x) between 0 and 2 pi to find the area between the graph and the axis but I keep getting 0, why?

(First draw graph of sin(x) and mark 0 and pi and 2 pi) In short, you will need to split up your integral into two parts. One from 0 to pi and one from pi to 2 pi? Can you see/guess why this might be? First ...
JB
Answered by Jack B. • Maths tutor
6667 Views

How do I solve the simultaneous equations x-2y=1 and x^2-xy+y^2=1?

Depending on what you prefer, you can either substitute or you can try to solve this by elimination. I'll explain both. 1) x - 2y = 1 2) x 2 - xy +y 2 = 1 If solving by elimination, you need to start thinkin...
KS
Answered by Katerina S. • Maths tutor
14543 Views

How do I calculate the 100th term of the sequence 15, 8, 1, -6...

A sequence means a pattern, so the first thing to do is find the pattern. First try seeing what the difference between the numbers is. 15-7=8, 8-7=1, 1-7=6, so the pattern must be to subtract 7 each time. Th...
KS
Answered by Katerina S. • Maths tutor
11691 Views

How do I find the derivative of 2^x?

To find the derivative of any number to the power &quot;x&quot;, such as 2 x , 5 x , or even 4.13 x , we first consider the general form a x . We need to be a little creative here. We know that any variable ...
KS
Answered by Katerina S. • Maths tutor
41610 Views